Singular perturbations and time scales in control theory and applications: An overview

Dynamics of Continuous, Discrete and Impulsive Systems Series B: Application and Algorithm

Volumn 9, Issue 2, 2002, Pages 233-278

  Naidu, D Subbaram ^a  

^a Nucl Eng Idaho State University   (United States)

Author keywords

Control systems; Control theory and applications; Order reduction; Singular perturbations; Time scales

Indexed keywords

EID: 0344339292     PISSN: 14928760     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Review

References (467)

1. M. Abbad and J. A. Filar. Algorithms for singularly perturbed limiting average Markov control problems. IEEE Transactions on Automatic Control, 37:1421-1425, September 1992.
2. M. Abbad and J. A. Filar. Algorithms for singularly perturbed markov control problems: A survey. In C. T. Leondes, editor, Control and Dynamic Systems: Advances in Theory and Applications, volume 73, pages 257-287. Academic Press, San Diego, CA, 1995.
3. E. H. Abed. Multiparameter singular perturbation problems: iterative expansions and asymptotic stability. Systems & Control Letters, 5:279-282, 1985.
4. E. H. Abed. A new parameter estimate in singular perturbations. Systems & Control Letters, 6:193-198, 1985.
5. E. H. Abed. Singularly perturbed Hopf bifurcation. IEEE Transactions on Circuits and Systems, CAS-12(12):1270-1280, December 1985.
6. E. H. Abed. Decomposition and stability of multiparameter singular perturbation problems. IEEE Transactions on Automatic Control, AC-31:925-934, 1986.
7. E. H. Abed. On the stability of multiple time-scale systems. International. Journal of Control, 44:211-218, 1986.
8. E. H. Abed. Strong D-stability. Systems & Control Letters, 7:207-212, 1986.
9. Z. Aganović and Z. Gajić. Linear Optimal Control of Bilinear Systems with Applications to Singular Perturbations and Weak Coupling, volume 206 of Lecture Notes in Control and Information Sciences. Springer-Verlag, London, UK, 1995.
10. S. Albeverio and P. Kurasov. Singular Perturbations of Differential Operators: Solvable Schrödinger Type Operators. London Mathematical Society Lecture Note Series, Vol. 271. Cambridge University Press, Cambridge, UK, 2000.
11. R. W. Aldhaheri and H. K. Khalil. A real Schur form method for modeling singularly perturbed systems. IEEE Transactions on Automatic Control, 34(8):856-861, August 1989.
12. J. Alvarez-Gallegos and G. Silva-Navarro. Two-time scale sliding-mode control for a class of nonlinear systems. International Journal of Robust and Nonlinear Control, 7:865-879, 1997.
13. J. G. Andrews and D. R. Atthey. Hydrodynamic limit to penetration of a material by a high power beam. Journal of Physics D: Applied Physics, 9:2181-2194, 1976.
14. O. D. Anosova. On invariant manifolds in singularly perturbed systems. Journal of Dynamical and Control Systems, 5(4):501-507, 1999.
15. M. D. Ardema, editor. Singular Perturbations in Systems and Control. Springer-Verlag, Wien, Austria, 1983.
16. M. D. Ardema. Computational singular perturbation method for dynamical systems. Journal of Guidance, Control, and Dynamics, 14(3):661-664, 1991.
17. M. D. Ardema and H. C. Chou. Second order algorithm for time optimal control of a linear system. In R. Bulrisch and D. Kraft, editors, Computational Optimal Control, pages 117-126. Birkhäuser Verlag, Boston, MA, 1994.
18. M. D. Ardema and E. Cooper. Singular perturbation time-optimal controller for disk drives. In R. Bulrisch, A. Miele, J. Stoer, and K. H. Well, editors, Optimal Control, pages 251-263. Birkhäuser Verlag, Boston, MA, 1993.
19. Z. Artstein and V. Gaitsgory. Tracking fast trajectories along slow dynamics: a singular perturbation approach. SIAM Journal of Control and Optimization, Section A: 126:541-569, 1999.
20. Z. Artstein and A. Vigodner. Singularly perturbed ordinary differential equations with dynamic limits. Proceedings of Royal Society of Edinburgh, 35(5):1487-1507, 1997.
21. A. Ashyaralyev and H. O. Fattorini. On uniform difference schemes for second-order singular perturbation problems. SIAM Journal of Mathematical Analysis, 23:29-54, January 1992.
22. A. N. Atassi and H. K. Khalil. A separation principle for the stabilization of a class of nonlinear systems. IEEE Transactions on Automatic Control, 44:1672-1687, September 1999.
23. A. N. Atassi and H. K. Khalil. Separation results for the stabilization of nonlinear systems using different high-gain observer designs. Systems & Control Letters, 39:183-191, March 2000.
24. M. R. Azimi-Sadjadi and K. Khorasani. Reduced-order strip Kalman filtering using singular perturbation method. IEEE Transactions on Circuits and Systems, 37:284-290, 1990.
25. M. R. Azimi-Sadjadi and K. Khorasani. A model reduction method for a class of 2D systems. IEEE Transactions on Circuits and Systems, 39:28-41, 1992.
26. ∞-Optimal Control and Related Minimax Design Problems: Second Edition. Birkhäuser, Boston, MA, 1995.
27. F. Bagagiolo and M. Bardi. Singular perturbation of a finite horizon problem with state-space constraints. SIAM Journal of Control and Optimization, 36(6):2040-2060, November 1998.
28. J. P. Barbot, M. Djemai, S. Manaco, and D. Normand-Cyrot. Analysis and control of nonlinear singularly perturbed systems with sampling. In C. T. Leondes, editor, Control and Dynamic Systems, pages 203-246. Academic Press, San Diego, CA, 1996.
29. J. W. Barker. Interaction of fast and slow waves in problems with two-time scales. Journal of Mathematical Analysis and Applications, 15:500-513, 1984.
30. L. Beji and A. Abichou. A singular perturbation approach for tracking control of a parallel robot including motor dynamics. International Journal of Control, 68:689-707, 1997.
31. C. M. Bender and S. A. Orszag. Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory. Springer-Verlag, New York, NY, 1999.
32. A. Bensoussan, editor. Perturbation Methods in Optimal Control. John Wiley & Sons, Chichester, UK, 1988.
33. A. Bensoussan, G. L. Blankenship, and P. V. Kokotović, editors. Singular Perturbations and Optimal Control. Springer-Verlag, Berlin, Germany, 1984.
34. T. Bielecki and J. A. Filar. Singularly perturbed Markov control problems. Annals of Operations Research, 29:523-541, 1991.
35. T. Bielecki and L. Stettner. On ergodic control problems for singularly perturbed Markov processes. Applied Mathematics and optimization, 20:131-161, 1989.
36. M. V. Bikdash, A. H. Nayfeh, and E. M. Cliff. Singular perturbation of the time-optimal soft-constrained cheap control problem. IEEE Transactions on Automatic Control, 38(3):466-469, March 1993.
37. H. S. Binning and D. P. Goodall. Output feedback control for a class of singularly perturbed uncertain systems. Automation and Remote Control, 58:1132-1145, July 1997.
38. H. S. Binning and D. P. Goodall. Constrained output feedbacks for singularly perturbed imperfect known nonlinear systems. Journal of Franklin Institute, 336:449-472, 1999.
39. H. S. Binning and D. P. Goodall. Constrained feedback control of imperfectly known singularly perturbed non-linear systems. International Journal of Control, 73:49-62, 2000.
40. L. E. Bobisud, D. O'Regan, and W. D. Royalty. Steady-state reaction-diffusion-convection equations: dead cores and singular perturbations. Nonlinear Analysis: Theory, Methods & Applications, 3:527-538, 1987.
41. I. Borno. Boundary value problems of linear discrete-time singularly perturbed systems. Control Theory and Advanced Technology, 10:923-928, December 1994.
42. R. Bouyekhf and A. El Moudni. On analysis of discrete singularly perturbed non-linear systems: application to the study of stability properties. Journal of Franklin Institute, 3346:199-212, 1997.
43. R. Bouyekhf and A. El Moudni. Stabilization and regulation of class of non-linear singularly perturbed discrete-time systems. Journal of Franklin Institute, 335B:963-982, 1998.
44. R. Bouyekhf, A. El Moudni, A. El Hami, N. Zerhouni, and M. Ferney. Reduced order modeling of two-time-scale discrete nonlinear systems. Journal of Franklin Institute, 333(B):499-512, 1996.
45. A. Bradshaw, K. L. Mak, and B. Porter. Singular perturbation methods in the synthesis of control policies for production-inventory systems. International Journal of Systems Science, 13:589-600, 1982.
46. J. H. Braslavsky, M. M. Seron, D. Q. Mayne, and P. V. Kokotović. Limiting performance of optimal linear filters. Automatica, 35:189-199, 1999.
47. F. Brezzi, A. C. Capelo, and L. Gastaldi. A singular perturbation analysis of reverse-based semiconductor diodes. SIAM Journal of Mathematical Analysis, 20:372-387, March 1989.
48. A. E. Bryson Jr. . Dynamic Optimization. Addison Wesley Longman, Inc., Menlo Park, CA, 1999.
49. A. W. Bush. Perturbation Methods for Engieers and Scientists. CRC Press, Boca Raton, FL, 1992.
50. V. F. Butuzov, A. B. Vasil'eva, and M. V. Fedoryuk. Asymptotic methods in the theory of ordinary differential equations. In R. V. Gamkrelidge, editor, Progress in Mathematics, volume 8, pages 1-82. Plenum Publishing, New York, New York, 1970. (Review article with 504 references).
51. A. J. Calise. Singular perturbations in flight mechanics. In A. Miele and A. Salvetti, editors, Applied Mathematics in Aerospace Science and Engineering, pages 115-132. Plenum Press, New York, New York, 1994.
52. A. J. Calise and J. E. Corban. Optimal control of two-time-scale systems with state-variable inequality constraints. Journal of Guidance, Control, and Dynamics, 15(2):468-476, March-April 1992.
53. A. J. Calise and D. D. Moerder. Optimal output feedback design of systems with ill-conditioned dynamics. Automatica, 21(3):271-276, 1985.
54. A. J. Calise, J. V. R. Prasad, and B. Siciliano. Design of output feedback compensators in two-time scale systems. IEEE Transactions on Automatic Control, 35(4):488-492, April 1990.
55. G. Capriz and G. Cimmatti. On some singular perturbation problems in the theory of lubrication. Applied Mathematics and Applications, 4:287-297, 1978.
56. K. W. Chang. Diagonalization method for a vector boundary value problem of singular perturbation type. Journal of Mathematical Analysis and Applications, 48:652-665, 1974.
57. K. W. Chang and F. A. Howes. Nonlinear Singular Perturbation Phenomena: Theory and Application. Springer-Verlag, New York, New York, 1984.
58. F. Chaplais and K. Alaoui. Two time scaled parameter identification by coordination of local identifiers. Automatica, 32:1303-1309, 1996.
59. B. S. Chen and C. L. Lin. On the stability bounds of singularly perturbed systems. IEEE Transactions on Automatic Control, 35:1265-1268, 1990.
60. C. C. Chen. Global exponential stabilization for nonlinear singularly perturbed systems. IEE Proceedings: Control Theory and Applications, 145:377-382, July 1998.
61. C.-P. Cheng, T. S. Li, and Y.-Y. Sun. Stability margins of singularly perturbed discrete-time systems based on state feedback and linear quadratic optimal control. Optimal Control: Applications & Methods, 13:227-245, 1992.
62. J.-S. Chiou, F.-C. Kung, and T.-H. S. Li. Robust stabilization of singularly perturbed discrete bilinear systems. IEEE Transactions on Automatic Control, 45:1187-1191, June 2000.
63. G. K. Choudhary, N. P. Singh, and Y. P. Singh. Two-time-scale discrete-time modeling and decomposition of synchronous machines. International Journal of Systems Science, 26:1029-1039, 1995.
64. J. H. Chow. Time-Scale Modeling of Dynamic Networks with Applications to Power Systems, volume 46 of Lecture Notes in Control and Information Sciences. Springer-Verlag, Berlin, Germany, 1982.
65. J. H. Chow and C. J. Hanley. Singular perturbation analysis of high-frequency filter design. International Journal of Control, 51:705-720, 1990.
66. J. H. Chow and P. V. Kokotović. Time scale modeling of sparse dynamic networks. IEEE Transactions on Automatic Control, AC-30:714-722, August 1985.
67. P. D. Christofides. Robust output feedback control of nonlinear singularly perturbed systems. Automatica, 36:45-52, 2000.
68. P. D. Christofides and P. Daoutidis. Compensation of measurable disturbances for two-time-scale nonlinear systems. Automatica, 32:1553-1573, 1996.
69. P. D. Christofides and P. Daoutidis. Feedback control of two-time-scale nonlinear systems. International Journal of Control, 63:965-994, 1996.
70. P. D. Christofides and P. Daoutidis. Robust control of multivariable two-time-scale nonlinear systems. Journal of Process Control, 7:313-328, 1997.
71. P. D. Christofides and A. R. Teel. Singular perturbations and input-to-state stability. IEEE Transactions on Automatic Control, 41:1645-1650, 1996.
72. P. D. Christofides, A. R. Teel, and P. Daoutidis. Robust semi-global output tracking for nonlinear singularly perturbed systems. International Journal of Control, 65:639-666, 1996.
73. L. O. Chua and H. Oka. Normal forms for constrained nonlinear differential equations - Part I: Theory. IEEE Transactions on Circuits and Systems, 35:881-901, 1988.
74. L. O. Chua and H. Oka. Normal forms for constrained nonlinear differential equations - Part II: Bifurcation. IEEE Transactions on Circuits and Systems, 35:881-901, 1989.
75. C.-H. Chuang, J. L. Speyer, and J. V. Breakwell. An asymptotic expansion for an optimal relaxation oscillator. SIAM Journal of Control and Optimization, 26:678-696, 1988.
76. B. Clapperton, F. Crusca, and M. Aldeen. Bilinear transformation and generalized singular perturbation model reduction. IEEE Transactions on Automatic Control, 41:589-593, 1996.
77. E. M. Cliff, K. H. Well, and K. Schnepper. Flight test guidance for airbreathing hypersonic vehicles. In Proceedings of the AIAA Guidance, Navigation and Control Conference, pages 1-6, Hilton Head, SC, August 1992. AIAA-92-4301.
78. J. D. Cobb. Global analyticity of a geometric decomposition for linear singularly perturbed systems. Circuits, Systems and Signal Processing, 5:139-152, 1986.
79. J. D. Cobb. Toward a theory of robust compensation for systems with unknown parasitics. IEEE Transactions on Automatic Control, 33:1130-1138, December 1988.
80. J. D. Cole. Perturbation methods in Applied Mathematics. Blaisdell, Waltham, MA, 1968.
81. M. Corless. Asymptotic stability of singularly perturbed systems which have marginally stable boundary layer systems. Journal of Dynamics and Control, 1(1):95-108, March 1991.
82. M. Corless. Control of uncertain systems. Transactions of ASME, Journal of Dynamic Systems, Measurement, and Control, 115:362-372, 1993.
83. M. Corless, F. Garofalo, and L. Gilielmo. New results on composite control of singularly perturbed uncertain linear systems. Automatica, 29:387-400, 1993.
84. M. Corless and L. Gilielmo. On the exponential stability of singularly perturbed systems. SIAM Journal of Control and Optimization, 30:1338-1360, 1992.
85. C. Coumarbatch and Z. Gajić. Exact decomposition of the algebraic Riccati equation of deterministic multimodeling optimal control problems. IEEE Transactions on Automatic Control, 45:790-794, 2000.
86. A. M. Dabroom and H. K. Khalil. Output feedback sampled-data control of nonlinear systems using high-gain observers. IEEE Transactions on Automatic Control, 40:1712-1725, November 2001.
87. G. Dauphin-Tanguy and P. Borne. Order reduction of multi-time scale systems using bond graphs, the reciprocal system and the singular perturbation method. Journal of the Franklin Institute, 319:157-171, January/February 1985.
88. N. Derbel, A. Oual, and M. B. Kamoun. Two step three time scale reduction of doubly fed machine models. IEEE Transactions on Energy Conversion, 9:77-84, March 1994.
89. C. A. Desoer and S. M. Shahruz. Stability of nonlinear systems with three-time scales. Circuits, Systems, and Signal Processing, 5:449-464, 1986.
90. A. A. Desrochers, editor. Intelligent Robotic Systems for Space Exploration. Kluwer Academic Publishers, Boston, Massachusetts, 1992.
91. D. Dicker and D. K. Babu. A singular perturbation problem in unsteady ground water flows with a free surface. International Journal of Engineering Science, 12:967-980, 1974.
92. A. L. Dontchev, Tz. Dontchev, and I. Slavov. A Tikhonov-type theorem for singularly perturbed differential inclusion. Nonlinear Analysis, Theory & Applications, 26(9):1547-1554, 1996.
93. A. L. Dontchev and I. Slavov. Lipschitz properties of the attainable set of singularly perturbed linear systems. Systems & Control Letters, 11:385-391, 1988.
94. A. L. Dontchev and V. M. Veliov. Singular perturbations in linear control systems with weakly coupled stable and unstable fast subsystems. Journal of Mathematical Analysis and Applications, 110:1-30, 1985.
95. V. Drǎgan. Observers with several time scales for systems with several time scales. International Journal of Control, 42:149-153, 1985.
96. V. Drǎgan. Asymptotic expansions for game theoretic Riccati equations and stabilization with disturbance attenuation for singularly perturbed systems. Systems and Control Letters, 20:455-463, 1993.
97. ∞-norm and disturbance attenuation for systems with fast transients. IEEE Transactions on Automatic Control, 41:747-750, 1996.
98. V. Drǎgan. The asymptotic behavior of the stability radius for a singularly perturbed linear system. International Journal of Robust and Nonlinear Control, 8:817-829, 1998.
99. V. Drǎgan and A. Halanay. High-gain feedback stabilization of linear systems. International Journal of Control, 45:549-577, 1987.
100. ∞ approach. Automatica, 35:1369-1378, August 1999.
101. P. Dupuis and H. J. Kushner. Stochastic systems with small noise, analysis and simulation: a phase locked loop example. SIAM Journal of Applied Mathematics, 47:643-661, June 1987.
102. M. Van Dyke. Perturbation Methods in Fluid Mechanics. Academic Press, New York, NY, 1964.
103. W. Eckhaus. Matched Asymptotic Expansions and Singular Perturbations. North Holland Publishing Company, Amsterdam, The Netherlands, 1973.
104. W. Eckhaus. Asymptotic Analysis of Singular Perturbations. North Holland Publishing Company, Amsterdam, The Netherlands, 1979.
105. W. Eckhaus and E. M. de Jager, editors. Theory and Applications of Singular Perturbations. Lecture Notes in Mathematics, Vol. 942, Springer-Verlag, Berlin, Germany, 1982.
106. W. Eckhaus, A. V. Harten, and Z. Peradzynski. A singularly perturbed free boundary value problem describing a laser sustained plasma. SIAM Journal of Applied Mathematics, 45:1-31, 1985.
107. E. Eitelberg. A transformation of non-linear dynamical systems with a single singular singularly perturbed differential equation, International Journal of Control, 41:1301-1316, 1985.
108. M. El-Ansary and H. Khalil. On the interplay of singular perturbations and wideband stochastic fluctuations. SIAM Journal of Control and Optimization, 24:83-94, January 1985.
109. S. V. Emelyanov, S. K. korovin, and I. G. Mamedov. Discrete singularly perturbed dynamical systems. In S. V. Emelyanov, editor, Variable Structure Control Systems: Discrete and Digital, pages 177-233. CRC Press, Boca Raton, FL, 1995. (Translated from Russian).
110. A. Erdélyi. Asymptotic Expansions. Dover Publications, New York, New York, 1956.
111. F. Esfandiari and H. K. Khalil. On the robustness of sampled-data control to unmodeled high-frequency dynamics. IEEE Transactions on Automatic Control, 34:900-903, August 1999.
112. B. F. Esham and R. J. Weinacht. Singular perturbations and the coupled/quasi-static approximation in linear thermoelasticity. SIAM Journal of Mathematical Analysis, 25:1521-1536, November 1994.
113. Z. Fathi and W. F. Ramirez. Joint state and parameter estimation for a nuclear reactor with fast and slow modes. Optimal Control: Applications & Methods, 13:105-120, 1992.
114. H. O. Fattorini. On Schrödinger singular perturbation problem. SIAM Journal of Mathematical Analysis, 16(5):1000-1019, September 1985.
115. W. Feng. Characterization and computation for the bound ε* in linear time-invariant singularly perturbed systems. Systems & Control Letters, 1:195-202, 1988.
116. J. A. Filar, V. Gaitsgory, and A. B. Haurie. Control of singularly perturbed hybrid stochastic systems. IEEE Transactions on Automatic Control, 46:179-190, February 2001.
117. J. E. Flaherty and R. E. O'Malley, Jr. Singularly perturbed boundary value problems for nonlinear systems including a challenging problem for a nonlinear beam. In W. Eckhaus and E. M. de Jager, editors, Theory and Applications of Singular Perturbations, pages 170-191. Springer-Verlag, Berlin, Germany, 1982.
118. L. S. Frank, editor. Singular Perturbations I: Spaces and Singular Perturbations on Manifolds without Boundary. Elsevier Science Publishers, Amsterdam, The Netherlands, 1990.
119. A. R. Fraser and R. W. Daniel, editors. Perturbation Techniques for Flexible Manipulators. Kluwer Academic Publishers, Boston, Massachusetts, 1991.
120. E. Fridman. Asymptotics of integral manifold and decomposition of singularly perturbed systems of neutral type. Differential Equations, 26:457-467, 1990.
121. E. Fridman. Decomposition of linear optimal singularly perturbed systems with time delay. Automation and Remote Control, 51:1518-1527, 1990.
122. ∞-optimal control problem. Kybernetika, 31:591-599, 1995.
123. E. Fridman. Decoupling transformation of singularly perturbed systems with small delays and its applications. ZAMM, 76:201-204, 1996.
124. ∞ control of linear singularly perturbed systems. IEEE Transactions on Automatic Control, 41:236-240, 1996.
125. E. Fridman. Exact slow-fast decomposition of a class of non-linear singularly perturbed optimal control problems via invariant manifolds. International Journal of Control, 72:1609-1618, 1999.
126. E. Fridman. Exact slow-fast decomposition of the non-linear singularly perturbed optimal control problem. Systems & Control Letters, 40:121-131, 2000.
127. ∞ control of nonlinear singularly perturbed systems. International Journal of Robust and Nonlinear Control, 11:1115-1125, 2001.
128. ∞ minimum entropy static output-feedback control of singularly perturbed systems. Automatica, 36:1181-1188, 2000.
129. E. Fridman and V. Strygin. Asymptotics of integral manifolds of singularly perturbed differential equations with a retarded argument. Mathematische Nachrichten, 117:83-109, 1984.
130. S. J. Fu and M. E. Sawan. On the reduced-order model for control-system design and analysis. International Journal of Systems Science, 117:319-324, 1986.
131. V. Gaitsgory. Suboptimization of singularly perturbed control systems. SIAM Journal of Control & Optimization, 30(5):1228-1249, September 1992.
132. V. Gaitsgory. Suboptimal control of singularly perturbed systems and periodic optimization. IEEE Transactions on Automatic Control, 38:888-903, June 1993.
133. V. Gaitsgory. Limit Hamilton-Jacobi-Isaacs equations for singularly perturbed zero-sum differential games. Journal of Mathematical Analysis and Applications, 202:862-899, 1996.
134. V. Gaitsgory and G. Grammel. On the construction of asymptotically optimal controls for singularly perturbed systems. Systems & Control Letters, 30:139-147, 1996.
135. Z. Gajić. Numerical fixed-point solution for near-optimum regulators of linear quadratic gaussian control problems for singularly perturbed systems. International Journal of Control, 43:373-387, 1986.
136. Z. Gajić. Well-posedness of a model order reduction for singularly perturbed linear stochastic systems. Optimal Control: Applications & Methods, 8:305-309, 1987.
137. Z. Gajić and H. K. Khalil. Multimodel strategies under random disturbances and imperfect partial observation. Automatica, 22:121-125, 1986.
138. Z. Gajić and M. Lim. Optimal Control of Singularly Perturbed Linear Systems and Applications: High-Accuracy Techniques. Marcel Dekker, Inc., New York, New York, 2001.
139. Z. Gajić, M. Lim, and X. Shen. The study of discrete singularly perturbed linear-quadratic control systems. In C. T. Leondes, editor, Control and Dynamic Systems: Advances in Theory and Applications, volume 70, pages 309-317. Academic Press, San Diego, CA, 1995.
140. Z. Gajić, D. Petrovski, and N. Harkara. The recursive algorithm for the optimal static output feedback control problem of linear singularly perturbed system. IEEE Transactions on Automatic Control, AC-34:465-468, 1989.
141. Z. Gajić, D. Petrovski, and X. Shen. Singularly Perturbed and Weakly Coupled Linear Control Systems: A Recursive Approach, volume 140 of Lecture Notes in Control and Information Sciences. Springer-Verlag, New York, New York, 1990.
142. Z. Gajić and X. Shen. Parallel reduced-order controllers for stochastic linear singularly perturbed discrete systems. IEEE Transactions on Automatic Control, 36:871-90, January 1991.
143. Z. Gajić and X. Shen. Parallel Algorithms for Optimal Control of Large Scale Systems. Springer-Verlag, London, UK, 1993.
144. 2 guaranteed cost control for singularly perturbed uncertain systems. IEEE Transactions on Automatic Control, 43:1323-1329, 1998.
145. R. Gardner. Stability and Hopf bifurcation of steady state solutions of a singularly perturbed reaction-diffusion system. SIAM Journal of Mathematical Analysis, 23:99-149, 1992.
146. F. Garofalo. A composite control of a singularly perturbed uncertain system with slow non-linearities. International Journal of Control, 48:1979-1991, 1988.
147. F. Garofalo and G. Leitmann. A composite controller ensuring ultimate boundness for a class of singularly perturbed systems. Dynamics and Stability of Systems: An International Journal, 3:135-145, 1988.
148. F. Garofalo and G. Leitmann. Nonlinear composite control of a class of nominally linear singularly perturbed uncertain systems. In A. S. I. Zinober, editor, Deterministic Control of Uncertain Systems, pages 269-288. IEE Press, London, UK, 1990.
149. R. Genesio and M. Milanese. A note on the derivation and the use of reduced-order models. IEEE Transactions on Automatic Control, AC-21:118-122, February 1976. (Comprehensive set of 137 references).
150. F. Ghorbel, J. Y. Hung, and M. W. Spong. Adaptive control of flexible-joint manipulators. IEEE Control Systems Magazine, 9:9-13, 1989.
151. R. Ghosh, S. Send, and K. B. Datta. Method for evaluating stability bounds for discrete-time singularly perturbed systems. IEE Proceedings: Control Theory and Applications, 146:227-233, March 1999.
152. T. R. Gichev. Singular perturbations in a class of problems of optimal control with integral convex criterion. Journal of Applied Mathematics and Mechanics, 48:654-658, 1984.
153. J. Golec and G. Ladde. On multitime method and the rate of convergence for a class of singularly perturbed stochastic systems. Journal of Mathematical Systems, Estimation, and Control, 2:245-262, 1992.
154. G. Grammel. Singularly perturbed differential inclusion: an averaging approach. Set-Valued Analysis, 4:361-374, 1996.
155. G. Grammel. Averaging of singularly perturbed systems. Nonlinear Analysis, Theory, Methods & Applications, 28(11):1851-1997, 1997.
156. G. Grammel. Limits of nonlinear discrete-time control systems with fast subsystems. Systems & Control Letters, 36:277-283, 1999.
157. G. Grammel. Maximum principle for a hybrid system via singular perturbations. SIAM Journal of Control & Optimization, 37(4):1162-1177, May 1999.
158. G. Grammel and P. Shi. On the asymptotics of the Lyapunov spectrum under singular perturbation. IEEE Transactions on Automatic Control, 45:565-569, March 2000.
159. T. Grodt and Z. Gajić. The recursive reduced-order numerical solution of the singularly perturbed matrix differential Riccati equation. IEEE Transactions on Automatic Control, AC-33:751-754, 1988.
160. L. T. Grujić. On the theory and synthesis of nonlinear non-stationary tracking singularly perturbed systems. Control: Theory and Advanced Technology, 4:395-410, 1988.
161. L. T. Grujić, A. A. Martynyuk, and M. Ribbens-Pavella. Large Scale Systems Stability Under Structural and Singular Perturbations. Springer-Verlag, Berlin, Germany, 1987.
162. Z.-M. Gu, N. N. Nefedov, and R. E. O'Malley, Jr. On singular singularly perturbed initial value problems. SIAM Journal of Applied Mathematics, 49:1-25, February 1989.
163. I. J. Ha, A. K. Tugcu, and N. M. Boustany. Feedback linearizing control of vehicle longitudinal acceleration. IEEE Transactions on Automatic Control, 34(7):689-698, July 1989.
164. M. Hanmandlu, N. v. Suryanarayana, and A. K. Sinha. Multi-time-scale decomposition of a high-gain feedback system. International Journal of Control, 44:17-41, 1986.
165. N. Harkara, D. Petkovski, and Z. Gajić. Recursive algorithm for the optimal static output feedback control problem of linear weakly-coupled systems. International Journal of Control, 50:1-11, 1989.
166. A. Van Harten. Singularly perturbed systems of diffusion type and feedback control. Automatica, 20:79-91, 1984.
167. K. Hashtrudi-Zaid and Khorasani. Control of non-minimum phase singularly perturbed systems with applications to flexible-link manipulators. International Journal of Control, 63:679-7012, 1996.
168. B. S. Heck. Sliding mode control for singularly perturbed systems. International Journal of Control, 53:985-1001, 1991.
169. B. S. Heck and A. H. Haddad. Singular perturbation analysis of linear systems with scaled quantized control. Automatica, 24:755-764, 1988.
170. B. S. Heck and A. H. Haddad. Singular perturbation in piecewise-linear systems. IEEE Transactions on Automatic Control, 34:87-90, 1989.
171. J. W. Helton, F. D. Kronewitter, W. M. McEneaney, and M. Stankus. Singularly perturbed control systems using non-commutative computer algebra. International Journal of Robust and Nonlinear Control, 10:983-1003, 2000.
172. A. J. Hermans. Wave pattern of a ship sailing at low speeds. In W. Eckhaus and E. M. de Jager, editors, Theory and Applications of Singular Perturbations, volume 942, pages 181-194. Springer-Verlag, Berlin, Germany, 1982.
173. D. Hilhorst. A perturbed free boundary value problem arising in the physics of ionized gases. In W. Eckhaus and E. M. de Jager, editors, Theory and Applications of Singular Perturbations, pages 309-317. Springer-Verlag, Berlin, Germany, 1982.
174. E. Hinch. Perturbation Methods. Cambridge University Bridge, Cambridge, UK, 1991.
175. J. O. Hirschefelder, C. F. Curtis, and D. F. Campbell. The theory of flame propagation. Journal of Physical Chemistry, 34:324-330, 1953.
176. F. C. Hoppensteadt. An algorithm for approximate solutions to weakly coupled filtered synchronous control systems and nonlinear processes. SIAM Journal of Applied Mathematics, 43:834-843, 1983.
177. F. C. Hoppensteadt. Singular perturbation solutions of noisy systems. SIAM Journal of Applied Mathematics, 55:544-551, 1995.
178. Y. Hosono and M. Mimura. Localized cluster solutions of nonlinear degenerate diffusion equations arising in population dynamics. SIAM Journal of Mathematical Analysis, 20:845-869, 1989.
179. F.-H. Hsiao, S.-T. Pan, and J.-D. Hwang. D-stabilization control for discrete-time two-time-scale systems. IEEE Control Systems Magazine, 20:50-66, 2000.
180. F.-H. Hsiao, S.-T. Pan, and C. C. Teng. An efficient algorithm for finding the D-stability bound of discrete singularly perturbed systems with multiple time-delays. International Journal of Control, 72(1):1-17, 1999.
181. G. Ikegami. On network perturbations of electrical circuits and singular perturbation of dynamical systems. In P. Fischer and W. R. Smith, editors, Chaos, Fractals, and Dynamics, pages 197-212. Marcel Dekker Inc., New York, NY, 1985.
182. M. Ilic and J. Zaborszky. Dynamics and Control of Large Electric Power Systems. John Wiley & Sons, New York, NY, 1999.
183. P. A. Ioannou and P. V. Kokotović. Adaptive Systems with Reduced Models, volume 47 of Lecture Notes in Control and Information Sciences. Springer-Verlag, Berlin, Germany, 1983.
184. P. A. Ioannou and P. V. Kokotović. Instability analysis and improvement of robustness of adaptive control. Automatica, 20:583-594, 1984.
185. P. A. Ioannou and P. V. Kokotović. Decentralized adaptive control of interconnected systems with reduced-order models. Automatica, 21:401-412, 1985.
186. P. A. Ioannou and K. S. Tsakalis. A robust direct adaptive controller. IEEE Transactions on Automatic Controller, AC-31:1033-1043, 1986.
187. S. Jayasuriya. Servotracking for a class of multivariable systems with parasitics. International Journal of Control, 44:1549-1554, 1986.
188. S. Jayasuriya. Multivariable disturbance rejection tracking controllers for systems with slow fast modes. Transactions of ASME, Journal of Dynamic Systems, Measurement & Control, 109:363-369, 1987.
189. J. Jiang and S. X. C. Lou. Production control of manufacturing systems: a multiple time scale approach. IEEE Transactions on Automatic Control, 39:2292-2297, 1994.
190. J. L. Junkins. Introduction to Dynamics and Control of Flexible Structures. American Institute of Aeronautics and Astronautics, Inc., Washington, DC, 1993.
191. Y. Kabanov and S. Pergamenshchikov. On convergence of attainability sets for controlled two-scale stochastic linear systems. SIAM Journal of Control and Optimization, 35, 1997.
192. M. K. Kadalbajoo and Y. N. Reddy. Asymptotic and numerical analysis of singular perturbation analysis: a survey. Applied Mathematics and Computation, 30:223-259, 1989. (Review article with 134 references).
193. M. K. Kadalbajoo and A. Singh. Boundary-value techniques to solve linear state regulator problems. Journal of Optimization Theory and Applications, 63:91-107, 1989.
194. H. Kando. Model reduction for 2D separable denominator systems: a singularly perturbed approach. International Journal of Systems Science, 28:529-545, 1997.
195. H. Kando and T. Iwazumi. Multirate digital control design of an optimal
196. H. Kando and T. Iwazumi. State feedback controller design of two-time scale discrete systems via singular perturbation approach. International Journal of Systems Science, 18:1537-1554, 1987.
197. H. Kando, T. Iwazumi, and H. Ukai. Singular perturbation modeling of large scale systems with multi-time-scale property. International Journal of Control, 48:2361-2387, 1988.
198. S. Kaplun. Fluid Mechanics and Singular Perturbations. Academic Press, Now York, New York, 1967.
199. M. Kathirkamanayagan and G. S. Ladde. Diagonalization and stability of large-scale singularly perturbed systems. Journal of Mathematical Analysis and Applications, 135:38-60, 1988.
200. V. Kecman, S. Bingulac, and Z. Gajić. Eigenvector approach for order reduction of singularly perturbed linear-quadratic optimal control problems. Automatica, 35:151-158, 1999.
201. V. Kecman and Z. Gajić. Optimal control and filtering for nonstandard singularly perturbed linear systems. Journal of Guidance, Control and Dynamics, 22:362-365, March-April 1999.
202. H. J. Kelley. Aircraft maneuver optimization by reduced order approximation. In C. T. Leondes, editor, Control and Dynamic Systems, pages 131-178. Academic Press, New York, New York, 1973.
203. J. Kevorkian and J. D. Cole. Perturbation Methods in Mathematics. Springer-Verlag, New York, New York, 1981.
204. J. K. Kevorkian and J. D. Cole. Multiple Scale and Singular Perturbation Methods. Springer-Verlag, New York, New York, 1996.
205. H. Khalil. Nonlinear Systems. Prentice Hall, Englewood Cliffs, NJ, second edition, 1996.
206. H. Khalil. Two-time scale and averaging methods. In W. S. Levine, editor, The Control Handbook, pages 873-879. CRC Press, Boca Raton, FL, 1996.
207. H. K. Khalil. Output feedback control of linear two-time-scale systems. IEEE Transactions on Automatic Control, AC-32:784-792, September 1987.
208. H. K. Khalil. Stability analysis of nonlinear multiparameter singularly perturbed systems. IEEE Transactions on Automatic Control, AC-32:260-263, March 1987.
209. H. K. Khalil. Feedback control of nonstandard singularly perturbed systems. IEEE Transactions on Automatic Control, AC-34:1052-1060, 1989.
210. H. K. Khalil. On the design of robust servomechanisms for minimum phase nonlinear systems. International Journal of Robust and Nonlinear Control, 10:339-361, 2000.
211. ∞ control of two-time-scale systems. Systems & Control Letters, 19:35-42, 1992.
212. H. K. Khalil and Z. Gajić. Near optimum regulators for stochastic linear singularly perturbed systems. IEEE Transactions on Automatic Control, AC-29:531-544, 1984.
213. H. K. Khalil and Y. N. Hu. Steering control of singularly perturbed systems: a composite control approach. Automatica, 25(1):65-75, 1989.
214. H. K. Khalil and J. V. Medanic. Closed-loop Stackelberg strategies for singularly perturbed linear quadratic problems. IEEE Transactions on Automatic Control, AC-25:66-71, 1980.
215. K. Khorasani. On linearization of nonlinear singularly perturbed systems. IEEE Transactions on Automatic Control, AC-32:256-260, 1987.
216. K. Khorasani. Robust stabilization of non-linear systems with unmodeled dynamics. International Journal of Control, 50:827-844, 1989.
217. K. Khorasani. A slow manifold approach to linear equivalents of nonlinear singularly perturbed systems. Automatica, 25:301-306, 1989.
218. K. Khorasani and M. R. Azimi-Sadjadi. Feedback control of two-time-scale block implemented discrete-time systems. IEEE Transactions on Automatic Control, AC-32:69-73, 1987.
219. K. Khorasani and P. V. Kokotović. Feedback linearization of a flexible manipulator near its rigid body manifold. Systems & Controls Letters, 6:187-192, 1985.
220. K. Khorasani and P. V. Kokotović. A corrective feedback design for nonlinear systems with fast actuators. IEEE Transactions on Automatic Control, AC-31:67-69, 1986.
221. K. Khorasani and M. A. Pai. Asymptotic stability improvements of multiparameter nonlinear singularly perturbed systems. IEEE Transactions on Automatic Control, AC-30:802-804, 1985.
222. K. Khorasani and M. A. Pai. Asymptotic stability of nonlinear singularly perturbed systems using higher order corrections. Automatica, 21:717-727, 1985.
223. K. Khorasani and M. A. Pai. Two time scale decomposition and stability analysis of power systems. IEE Proceedings: Control Theory and Applications, 135:205-212, 1988.
224. C. Knessl, B. J. Matkowsky, Z. Schuss, and C. Tier. On the performance of state-dependent single server queues. SIAM Journal of Applied Mathematics, 46:657-697, 1986.
225. P. V. Kokotović. A Riccati equation for block-diagonalization of ill-conditioned systems. IEEE Transactions on Automatic Control, AC-20:812-814, 1975.
226. P. V. Kokotović. Applications of singular perturbation techniques to control problems. SIAM Review, 26:501-550, 1984. (Review article with about 250 references).
227. P. V. Kokotović. Recent trends in feedback design: an overview. Automatica, 21:225-236, 1985. (Review article with about 85 references).
228. P. V. Kokotović, A. Bensoussan, and G. Blankenship, editors. Singular Perturbations and Asymptotic Analysis in Control Systems, volume 90 of Lecture Notes in Control and Information Sciences. Springer-Verlag, Berlin, Germany, 1987.
229. P. V. Kokotović and H. K. Khalil, editors. Singular Perturbations in Systems and Control. IEEE Press, New York, NY, 1986. Reprint.
230. P. V. Kokotović, H. K. Khalil, and J. O'Reilly. Singular Perturbation Methods in Control: Analysis and Design. Academic Press, London, UK, 1986.
231. P. V. Kokotović, R. E. O'Malley, Jr., and P. Sannuti. Singular perturbations and order reduction in control theory-an overview. Automatica, 12:123-132, 1976. (Review article with about 125 references).
232. P. V. Kokotović and W. R. Perkins, editors. Singular Perturbations: Order Reduction in Control Systems Design. American Society of Mechanical Engineers, New York, New York, 1972.
233. P. V. Kokotović and P. Sannuti. Singular perturbation method for reducing model order in optimal control design. IEEE Transactions on Automatic Control, AC-13:377-384, 1968.
234. P. V. Kokotović and P. W. Sauer. Integral manifold as a tool for reduced-order modeling of nonlinear systems: a synchronous machine case study. IEEE Transactions on Automatic Control, 36:403-410, 1989.
235. H.-O. Kreiss, N. K. Nichols, and D. L. Brown. Numerical methods for stiff two-point boundary value problems. SIAM Journal of Numerical Analysis, 23:325-368, 1986.
236. K. V. Krikorian and C. T. Leondes. Dynamic programming using singular perturbations. Journal of Optimization Theory and Applications, 38:221-240, 1982.
237. H. Krishnan and N. H. McClamroch. On the connection between nonlinear differential-algebraic equations and singularly perturbed systems in nonstandard form. IEEE Transactions on Automatic Control, 39:1079-1084, 1994.
238. M. S. Krishnarayalu. Singular perturbation method applied to the open-loop discrete optimal control problem with two small parameters. International Journal of Systems Science, 20:793-809, 1989.
239. M. S. Krishnarayalu. Singular perturbation method applied to the closed-loop discrete optimal control problem. Optimal Control: Applications & Methods, 11:73-83, 1990.
240. M. S. Krishnarayalu. Singular perturbation analysis of a class of initial and boundary value problems in multiparameter digital control systems. Control - Theory and Advanced Technology, 10:465-477, 1994.
241. M. S. Krishnarayalu. Singular perturbation methods for one-point, two-point and multi-point boundary value problems in multiparameter digital control systems. Journal of Electrical and Electronics Engineering (Australia), 19:97-110, September 1999.
242. M. S. Krishnarayalu and D. S. Naidu. Singular perturbation method for boundary value problems in two parameter discrete control systems. International Journal of Systems Science, 19:2131-2143, 1988.
243. R. Krtilica. A singular perturbation model of reliability in system control. Journal of Optimization Theory and Applications, 20:51-57, 1984.
244. G. A. Kurina. Singular perturbations of control problems with equations of state not solved for the derivative (a survey). Journal of Computer and System Sciences International, 31(6):17-45, 1993. (135 references).
245. H. J. Kushner. Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems. Birkhäuser, Boston, MA, 1990.
246. H. J. Kushner and W. Runggaldier. Nearly optimal state feedback controls for stochastic systems with wideband noise disturbances. SIAM Journal on Control and Optimization, 25:298-315, 1987.
247. G. S. Ladde and S. G. Rajalakshmi. Diagonalization and stability of multi-time-scale singularly perturbed systems. Applied Mathematics and Computation, 16:115-140, 1985.
248. G. S. Ladde and S. G. Rajalakshmi. Singular perturbation of linear systems with multiparameter and multiple time scales. Journal of Mathematical Analysis and Applications, 129:457-481, 1988.
249. G. S. Ladde and O. Sirisaengtaksin. Multitime-scale singularly perturbed linear stochastic systems. Stochastic Analysis and Applications, 4:213-238, 1986.
250. P. A. Lagerstrom and R. G. Casten. Basic concepts underlying singular perturbation techniques. SIAM Review, 14:63-120, 1972. (survey with 25 references on the essential ideas and not on literature).
251. S. H. Lam and D. A. Goussis. Basic theory and demonstration of computational singular perturbation for stiff equations. In Proceedings of the 12th IMACS World Congress on Scientific Computation, pages 487-492, Paris, France, 1989.
252. S. H. Lam and D. A. Goussis. The CSP method for simplifying kinetics. International Journal of Chemical Kinetics, 26:461-486, 1994.
253. S. H. Lan. Singular perturbation for stiff equations using numerical methods. In C. Casci, editor, Recent Advances in Aerospace Sciences, pages 3-19. Plenum Press, New York, NY, 1985.
254. J. T. Lee and Z. N. Bien. A quadratic regulator with cheap control for a class of nonlinear systems. Journal of Optimization Theory and Applications, 55:289-302, 1987.
255. B. Lennartson. Multirate sampled data control of two-time-scale systems. IEEE Transactions on Automatic Control, 34:642-644, 1989.
256. T. H. S. Li, J. S. Chiou, and F. C. Kung. Stability bounds of singularly perturbed discrete systems. IEEE Transactions on Automatic Control, 44:1934-1938, October 1999.
257. T. H. S. Li and J. H. Li. Stabilization bound of discrete two-time-scale systems. Systems & Control Letters, 18:479-189, 1992.
258. T.-H. S. Li and J. H. Li. Optimal static output feedback stabilization of singularly perturbed discrete-time systems. IMA Journal of Mathematical Control & Information, 11:213-230, 1994.
259. T. H. S. Li and J. H. Li. On the composite and reduced observer-based control of discrete two-time-scale systems. The Journal of Franklin Institute, 332:47-66, 1995.
260. T. H. S. Li and Y.-Y. Sun. A new stabilizing state-feedback control of singularly perturbation systems. Control Theory: Advanced Technology, 4:465-472, December 1988.
261. T. H. S. Li, M.-S. Wang, and Y.-Y. Sun. Robust dynamic output feedback sliding-mode control of singular perturbation systems. JSME International Journal, 38:719-728, 1995.
262. T. H. S. Li, M.-S. Wang, and Y.-Y. Sun. Dynamic output feedback design for singularly perturbed discrete systems. IMA Journal of Mathematical Control & Information, 13:105-115, 1996.
263. A. Liakopoulos and Jr. W. H. Boykin. Singular perturbation analysis of speed controlled reciprocating compressors. Transaction of ASME, Journal of Dynamic Systems, Measurement, and Control, 111:313-321, 1989.
264. C.-L. Lin and B.-S. Ghen. On the design of stabilizing controllers for singularly perturbed systems. IEEE Transactions on Automatic Control, 37:1828-1834, November 1992.
265. B. Litkouhi and H. K. Khalil. Infinite time regulators for singularly perturbed difference equations. International Journal of Control, 39:567-598, 1984.
266. B. Litkouhi and H. K. Khalil. Multirate and composite control of two-time-scale discrete-time systems. IEEE Transactions on Automatic Control, AC-30:645-651, 1985.
267. W. Q. Liu, M. Paskota, V. Sreeram, and K. L. Teo. Improvement on stability bounds for singularly perturbed systems via state feedback. International Journal of Systems Science, 28:571-578, 1996.
268. Y. Liu and B. D. O. Anderson. Singular perturbation approximation of balanced systems. International Journal of Control, 50:1379-1405, 1989.
269. X.-C. Lou, A. S. Willsky, and G. C. Verghese. Algebraic approach to time scale analysis of singularly perturbed linear systems. International Journal of Control, 47:281-308, 1988.
270. D. W. Luse. Frequency domain results for systems with multiple time scales. IEEE Transactions on Automatic Control, AC-31:918-924, October 1986.
271. D. W. Luse. State-space realization of multiple-frequency-scale transfer matrices. IEEE Transactions on Automatic Control, AC-31:185-187, February 1988.
272. ∞-disk problems. SIAM Journal on Control and Optimization, 27:814-835, July 1989.
273. D. W. Luse and H. K. Khalil. Frequency domain results for systems with slow and fast dynamics. IEEE Transactions on Automatic Control, AC-30:1171-1179, December 1985.
274. M. Mahmoud. Stabilization of discrete systems with multiple-time scales. IEEE Transactions on Automatic Control, AC-31:159-162, February 1986.
275. M. S. Mahmoud. Discrete systems with multiple scales. In C. T. Leondes, editor, Control and Dynamic Systems: Advances in Theory and Applications, volume 27, pages 307-367. Academic Press, San Diego, CA, 1988.
276. M. S. Mahmoud. Algorithms for discrete systems with multi-time scales. In C. T. Leondes, editor, Control and Dynamic Systems: Advances in Theory and Applications, volume 30, pages 217-245. Academic Press, San Diego, CA, 1989.
277. M. S. Mahmoud, A. S. Al-Fuhaid, and F. A. Saleh. Reduced-order performance of adaptive control systems. Applied Mathematics and Modeling, 11:133-140, April 1987.
278. M. S. Mahmoud, Y. Chen, and M. G. Singh. Discrete two-time-scaloe systems. International Journal of Systems Science, 17:1187-1207, 1986.
279. M. S. Mahmoud, H. A. Othman, and N. M. Khraishi. Reduced-order performance of adaptive control systems. IEEE Transactions on Automatic Control, AC-31:1076-1079, 1986.
280. M. S. Mahmoud and M. G. Singh. Discrete Systems: Analysis, Control, and Optimization. Springer-Verlag, Berlin, Germany, 1984.
281. M. S. Mahmoud and M. G. Singh. A two-stage output feedback design. IEE Proceedings, Part D: Control Theory and Applications, 133:279-284, 1986.
282. S. B. Margolis and B. J. Matkowsk. Flame propagation with multiple fuels. SIAM Journal of Applied Mathematics, 42:982-1003, 1982.
283. R. Marino. High-gain feedback in nonlinear control systems. International Journal of Control, 42:1369-1385, 1985.
284. R. Marino and P. V. Kokotovic. A geometric approach to nonlinear singularly perturbed control systems. Automatica, 24:31-41, 1988.
285. R. Marino and S. Nicosia. On the feedback control of industrial robots with elastic joints: A singular perturbation approach. Technical Report R84. 01, University of Rome, Rome, Italy, 1984.
286. R. Marino, W. Respondek, and A. J. Van Der Schaft. Direct approach to almost disturbance and almost input-output decoupling. International Journal of Control, 48:353-383, 1988.
287. R. Marino, W. Respondek, and A. J. Van Der Schaft. Almost disturbance decoupling for single-input and single-output nonlinear systems. IEEE Transactions on Automatic Control, 34:1013-1017, 1989.
288. P. A. Markowich. A singular perturbation analysis of the fundamental semiconductor device equation. SIAM Journal of Applied Mathematics, 44:896-928, 1984.
289. P. A. Markowich and C. A. Ringhofer. A singularly perturbed boundary value problem modeling a semiconductor device. SIAM Journal of Applied Mathematics, 44:231-256, 1984.
290. P. A. Markowich, C. A. Ringhofer, S. Selberherr, and M. Lentin. A singular perturbation approach for the analysis of the fundamental semiconductor equations. IEEE Transactions on Electron Devices, ED-30:1165-1181, 1983.
291. A. A. Martynuk. Uniform asymptotic stability of a singularly perturbed system via the Lyapunov-matrix function. Nonlinear Analysis, 11:1-4, 1987.
292. A. A. Martynyuk. Stability of Singularly Perturbed Systems, volume 214 of Pure and Applied Mathematics: A Series of Monographs and Textbooks, pages 127-176. Marcel Dekker, New York, NY, 1998.
293. B. J. Matkowsky and E. L. Reiss. Singular perturbations of bifurcations. SIAM Journal of Applied Mathematics, 33:230-255, 1977.
294. P. S. Maybeck and M. R. Schore, Reduced-order multiple model adaptive controller for flexible space structures. IEEE Transactions on Aerospace and Electronic Systems, 28:756-767, 1992.
295. N. H. McClamroch and H. Krishnan. Nonstandard singularly perturbed control systems and differential-algebraic equations. International Journal of Control, 55:1239-1253, 1992.
296. R. Meyer and S. V. Parter, editors. Singular Perturbations and Asymptotics. Academic Press, New York, NY, 1980.
297. R.H. Middleton and G.C. Goodwin. Digital Control and Estimation: A Unified Approach. Prentice Hall, Englewood Cliffs, NJ, 1990.
298. S.D. Milusheva and D. D. Bainov. Justification of the averaging method for a system of singularly perturbed differential equations with impulses. Journal of Applied Mathematical Physics (JAMP), 36:293-308, 1985.
299. E. F. Mishchenko and N. K. Rozo. Differential Equations with Small Parameters and Relaxed Oscillations. Plenum Publishing Company, New York, New York, 1980.
300. K. Mizukami and F. Suzumura. Closed-loop Stackelberg strategies for singularly perturbed systems: the recursive approach. International Journal of Systems Sciences, 24:887-900, 1993.
301. D. D. Moerder and A. J. Calise. Convergence of a numerical algorithm for calculating optimal output feedback gains. IEEE Transactions on Automatic Control, AC-30:900-903, 1985.
302. D. D. Moerder and A. J. Calise. Two-time-scale stabilization of systems with output feedback. Journal of Guidance, Control, and Dynamics, 8(6):731-736, November-December 1985.
303. D. D. Moerder and A. J. Calise. Near optimal output feedback regulation of ill-conditioned linear systems. IEEE Transactions on Automatic Control, AC-33:463-466, 1988.
304. P. M. Sharkey. Composite control of non-linear singularly perturbed systems meeting a design objective. International Journal of Control, 50:2173-2186, 1989.
305. P. M. Sharkey and J. O'Reilly. Exact design manifold control of a class of nonlinear singularly perturbed systems. IEEE Transactions on Automatic Control, AC-32:933-935, 1987.
306. H. Mukaidani and K. Mizukami. The guaranteed cost control problem of uncertain singularly perturbed systems. Journal of Mathematical Analysis and Applications, 251:716-735, 2000.
307. inf control problems for singularly perturbed systems under perfect and imperfect state measurements. International Journal of Systems Science, 30:467-477, 1999.
308. inf control problem of singularly perturbed systems. International Journal of Systems Science, 31:1299-1312, 2000.
309. inf control problem of singularly perturbed systems. IEEE Transactions on Automatic Control, 46(10):1659-1666, October 2001.
310. S. Murata, Y. Ando, and M. Suzuki. Design of a high gain regulator by the multiple time scale approach. Automatica, 26:585-591, 1990.
311. J. A. Murdock. Perturbations: Theory and Methods. John Wiley & Sons, New York, NY, 1991.
312. G. Musacato. Parametric generalized singular perturbation approximation for model order reduction. IEEE Transactions on Automatic Control, 45(2):339-343, February 2000.
313. D. S. Naidu. Singular Perturbation Methodology in Control Systems. Peter Peregrinus Limited, Stevenage Herts, UK, 1988.
314. D. S. Naidu. Aeroassisted Orbital Transfer: Guidance and Control Strategies, volume 188 of Lecture Notes in Control and Information Sciences. Springer-Verlag, London, UK, 1994.
315. D. S. Naidu. Guidance and control strategies for aeroassisted orbital transfer: status survey. In Proceedings of the AIAA Atmospheric Flight Mechanics Conference, Scottsdale, AZ, August 1-3 1994. (Review article with 20 important references).
316. D. S. Naidu. Singular perturbations and time scales in aerospace systems: An overview. In S. Sivasundaram, editor, Nonlinear Problems in Aviation and Aerospace, pages 251-263. Gordon and Breach Science Publishers, UK, 2000. (Review article with 84 references).
317. D. S. Naidu and A. J. Calise. Singular perturbations and time scales in control theory and applications: survey 1983-1989. In IFAC Workshop on Singular Perturbations and Asymptotic Methods in Systems and Control, Boston, MA, August 17-18 1989.
318. D. S. Naidu and A. J. Calise. Singular perturbations and time scales in guidance, navigation and control of aerospace systems: survey. In Proceedings of the AIAA Guidance, Navigation and Control Conference, pages 1338-1362, Baltimore, MD, August 7-10 1995. (Invited Survey Paper with 246 references).
319. D. S. Naidu and A. J. Calise. Singular perturbations and time scales in guidance and control of aerospace systems: survey. Journal of Guidance, Control and Dynamics, 24(6):1057-1078, November-December 2001. (Survey paper with 412 references).
320. D. S. Naidu and M. S. Krishnarayalu. Singular perturbation method for initial value problems in two-parameter discrete control systems. International Journal of Systems Science, 18:2197-2208, 1987.
321. D. S. Naidu and D. B. Price. Time scale synthesis of a closed-loop discrete optimal control system. Journal of Guidance, Control, and Dynamics, 10(5):417-421, 1987.
322. D. S. Naidu and D. B. Price. Singular perturbation and time scale approaches in discrete control systems. Journal of Guidance, Control, and Dynamics, 11(5):592-594, 1988.
323. D. S. Naidu, D. B. Price, and J. L. Hibey. Singular perturbations and time scales in discrete control systems-an overview. In Proceedings of The 26th IEEE Conf. on Decision and Control, pages 2096-2103, Los Angeles, CA, December 1987. (Invited survey paper with 121 references).
324. D. S. Naidu and P. K. Rajagopalan. Application of Vasil'eva's singular perturbation method to a problem in ecology. International Journal of Systems Science, 10:761-774, 1979.
325. D. S. Naidu and A. K. Rao. Singular perturbation analysis of closed loop discrete optimal control problem. Optimal Control: Applications and Methods, 5:19-28, 1984.
326. D. S. Naidu and A. K. Rao. Application of singular perturbation method to a steam power system. Electric Power Systems Research, 8:219-226, 1985.
327. D. S. Naidu and A. K. Rao. Singular Perturbation Analysis of Discrete Control Systems, volume 1154 of Lecture Notes in Mathematics. Springer-Verlag, New York, NY, 1985.
328. A. H. Nayfeh. A comparison of three perturbation methods for earth-moon-spaceship problem. AIAA Journal, 3(9):1682-1687, September 1965.
329. A. H. Nayfeh. Perturbation Methods. Wiley-Interscience, New York, NY, 1973.
330. A. H. Nayfeh. Introduction to Perturbation Techniques. John-Wiley & Sons, New York, NY, 1981.
331. A. H. Nayfeh. Problems in Perturbation. John-Wiley & Sons, New York, NY, 1985.
332. K. Nipp. Invariant manifolds of singularly perturbed ordinary differential equations. Journal of Applied Mathematical Physics (JAMP), 36:309-320, 1985.
333. N. Nordström. Order-reducing approximation of two-time-scale discrete linear time-varying systems. International Journal of Control, 46:731-751, 1987.
334. G. Obinata and B. D. O. Anderson. Model Reduction for Control System Design. Springer-Verlag, London, UK, 2001.
335. S. Oh and H. K. Khalil. Nonlinear output-feedback tracking using high-gain observer and variable structure control. Automatica, 33:1845-1856, 1997.
336. H. M. Oloomi and M. E. Sawan. The observer-based controller design of two-time singularly perturbed systems. IEEE Transactions on Automatic Control, 32:246-248, 1987.
337. H. M. Oloomi and M. E. Sawan. Characterization of zeros in two-frequency-scale systems. IEEE Transactions on Automatic Control, 40:92-96, 1995.
338. R. E. O'Malley, Jr. Topics in singular perturbations. In Advances in Mathematics, volume 2, pages 356-470. Academic Press, New York, New York, 1968. (Review article with 183 references).
339. R. E. O'Malley, Jr. Introduction to Singular Perturbations. Academic Press, New York, NY, 1974.
340. R. E. O'Malley, Jr. Singular Perturbation Methods for Ordinary Differential Equations. Springer-Verlag, New York, NY, 1991.
341. R. E. O'Malley, Jr. and C. Schmeiser. The asymptotic solution of a semiconductor device problem involving reverse bias. SIAM Journal of Applied Mathematics, 50:504-520, 1990.
342. J. O'Reilly. Robustness of linear feedback control systems to unmodeled high-frequency dynamics. International Journal of Control, 44:1077-1088, October 1986.
343. H. A. Othman, N. M. Khraishi, and M. S. Mahmoud. Discrete regulators with time-scale separation. IEEE Transactions on Automatic Control, AC-30:293-297, 1985.
344. A. A. Oyediran and J. A. Gbadeyan. Vibration of a prestressed orthotropic rectangular thin plate via singular perturbation technique. Acta Mechanica, 64:165-178, 1986.
345. S. T. Pan, F. H. Hsiao, and L. G. Hsiau. Composite feedback control of discrete multiparameter singularly perturbed systems. International Journal of Control, 69:577-597, 1998.
346. ∞-optimal control for singularly perturbed systems: Part I: perfect state measurements. Automatica, 29:401-423, 1993.
347. ∞-optimal control for singularly perturbed systems: Part II: imperfect state measurements. IEEE Transactions on Automatic Control, 39:280-299, 1994.
348. Z. Pan and T. Başar. Model simplification and optimal control of stochastic singularly perturbed systems under exponentiated quadratic cost. SIAM Journal of Control and Optimization, 34:1734-1766, 1996.
349. Z. Pan and T. Başar. Time-scale separation and robust controller design for uncertain nonlinear singularly perturbed systems under perfect state measurements. International Journal of Robust and Nonlinear Control, 6:585-608, 1996.
350. B. M. Patre, B. Bandyopadhyay, and H. Werner. Periodic output feedback control for singularly perturbed discrete model of a steam power system. IEE Proceedings-Control Theory and Applications, 146(3):247-252, May 1999.
351. D. C. Popescu and Z. Gajić. Singular perturbation analysis of cheap control problem for sampled data systems. IEEE Transactions on Automatic Control, 44(11):2209-2214, 1999.
352. R. Prakash and S. V. Rao. Model reduction by low frequency approximation of internally balanced representation. IEEE Transactions on Automatic Control, 39:1135-1141, May 1994.
353. B. Priel and U. Shaked. Cheap optimal control of discrete single input single output systems. International Journal of Control, 38:1087-11113, 1984.
354. M. Quincampoix and H. Zhang. Singular perturbations in non-linear optimal control problems. Differential and Integral Equations, 4:931-944, April 1995.
355. M. T. Qureshi, X. Shen, and Z. Gajić. Optimal output feedback control of a discrete linear, singularly perturbed stochastic systems. International Journal of Control, 55:301-371, 1992.
356. A. V. Rao and K. D. Mease. Dichomatic basis approach to solving hyper-sensitive optimal control problems. Automatica, 35:633-642, 1999.
357. A. V. Rao and K. D. Mease. Eigenvector approximate dichomatic basis method for solving hyper-sensitive optimal control problems. Optimal Control: Applications and Methods, 20:59-77, 1999.
358. K. R. Rao, L. Jenkins, K. Parthasarathy, and R. Balasubramanyam. Mutli-time scale analysis applied to long time simulation of power systems. Electric Power & Energy Systems, 7:7-12, 1985.
359. B. D. Riedle and P. V. Kokotović. Stability analysis of an adaptive system with unmodelled dynamics. International Journal of Control, 41:389-402, 1985.
360. C. Ringhofer. An asymptotic analysis of a transient p-n-junction model. SIAM Journal of Applied Mathematics, 47:624-642, 1987.
361. C. Ringhofer and C. Schmeiser. An approximate Newton method for the solution of the basic semiconductor equations. SIAM Journal of Numerical Analysis, 26:507-516; 1989.
362. N. Rudraih and T. Musuoka. Asymptotic analysis of natural convection through horizontal porous layer. International Journal of Engineering Science, 30:29-39, 1982.
363. A. Saberi. Output-feedback control with almost-disturbance-decoupling property-a singular perturbation approach. International Journal of Control, 45:1705-1722, 1987.
364. A. Saberi and H. K. Khalil. An initial value theorem for nonlinear singularly perturbed systems. Systems & Control Letters, 4:301-305, 1984.
365. A. Saberi and H. K. Khalil. Quadratic-type lyapunov functions for singularly perturbed systems. IEEE Transactions on Automatic Control, AC-29:542-550, 1984.
366. A. Saberi and H. K. Khalil. Stabilization and regulation of nonlinear singularly perturbed systems-composite control. IEEE Transactions on Automatic Control, AC-30:739-747, 1985.
367. A. Saberi and P. Sannuti. Cheap and singular controls for linear quadratic regulators. IEEE Transactions on Automatic Control, AC-32:2008-2019, 1987.
368. A. Saberi and P. Sannuti. Time-scale structure assignment in linear multivariable systems using high-gain feedback. International Journal of Control, 49:2191-2213, 1989.
369. V. R. Saksena and T. Başar. Multimodelling, singular perturbations and stochastic decision problems. In C. T. Leondes, editor, Control and Dynamic Systems, pages 1-58. Academic Press, New York, New York, 1986.
370. V. R. Saksena and J. B. Cruz. Robust Nash strategies for a class of nonlinear singularly perturbed problems. International Journal of Control, 39:293-310, 1984.
371. V. R. Saksena and J. B. Cruz. Optimal and near optimal incentive strategies in the hierarchical control of markov chains. Automatica, 21:181-191, 1985.
372. V. R. Saksena and J. B. Cruz. A unified approach to reduced order modelling and control of large scale systems with multiple decision makers. Optimal Control: Applications and Methods, 4:403-420, 1985.
373. V. R. Saksena, J. O'Reilly, and P. V. Kokotović. Singular perturbations and time-scale methods in control theory: survey 1976-1983. Automatica, 20:273-293, 1984. (Review article with about 350 references).
374. P. Sannuti. Singular perturbation method in the theory of optimal control PhD thesis, University of Illinois, Urbana-Champaign, 1968.
375. P. Sannuti and P. V. Kokotović. Near optimum design of linear systems by singular perturbation method. IEEE Transactions on Automatic Control, AC-14:15-22, 1969.
376. P. Sannuti and H. S. Wason. Multiple time-scale decomposition in cheap control problems-singular control. IEEE Transactions on Automatic Control, AC-30:633-644, 1985.
377. W. Sarlet. On a common derivation of the averaging method and the two-time-scale method. Celestial Mechanics, 17:299-312, 1978.
378. S. Sastry. Nonlinear Systems: Analysis, Stability, and Control. Springer-Verlag, New York, NY, 1999.
379. S. S. Sastry and J. Hauser. Zero dynamics of regularly perturbed systems may be singularly perturbed. Systems & Control Letters, 13:299-314, 1989.
380. L. Saydy. New stability/performance results for singularly perturbed systems. Automatica, 32:807-818, 1996.
381. B. M. Scherzinger and E. J. Davison. The optimal LQ regulator with cheap control for nonstrictly proper systems. Optimal Control: Applications & Methods, 6:291-303, 1985.
382. C. Schmeiser. Finite deformation of thin beams: asymptotic analysis by singular perturbation methods. IMA Journal of Applied Mathematics, 34:155-164, 1985.
383. C. Schmeiser. A singular perturbation analysis of a reverse biased pn - junctions. SIAM Journal of Mathematical Analysis, 21:313-326, 1990.
384. L. A. Segel and M. Slemrod. The quasi-steady-state assumption: a case study in perturbation. SIAM Review, 31:446-477, 1989.
385. S. Sen and K. B. Datta. Stability bounds of singularly perturbed systems. IEEE Transactions on Automatic Control, 38:302-304, 1993.
386. S. Sen and K. B. Datta. Time-optimal control algorithm for two-time-scale discrete systems-a multirate approach. Control Theory and Advanced Technology, 9:733-743, 1993.
387. S. Sen and D. S. Naidu. A time-optimal control algorithm for two-time scale discrete system. International Journal of Control, 47:1595-1602, 1988.
388. M. M. Seron, J. H. Braslavsky, P. V. Kokotović, and D. Q. Mayne. Feedback limitations in nonlinear systems: form Bode integrals to cheap control. IEEE Transactions on Automatic Control, 44:829-833, 1999.
389. S. P. Sethi and Q. Zhang. Hierarchical Decision Making in Stochastic Manufacturing Systems. Birkhäuser, Boston, MA, 1995.
390. X. Shen and Z. Gajić. Approximate parallel controllers for discrete stochastic weakly coupled linear systems. Optimal Control: Applications & Methods, 11:345-354, 1990.
391. X. Shen and Z. Gajić. Near-optimum steady state regulators for stochastic linear weakly coupled systems. Automatica, 26:919-923, 1990.
392. X. Shen, M. Rao, and Y. Ying. Decomposition method for solving Kalman filter gains in singularly perturbed systems. Optimal Control: Applications & Methods, 14:67-73, 1993.
393. X. Shen, Q. Xia, M. Rao, and Y. Ying. Near-optimum regulators for singularly perturbed jump systems. Control - Theory and Advanced Technology, 9:759-773, 1993.
394. ∞ control of singularly perturbed systems with parametric uncertainties. IEEE Transactions on Automatic Control, 44:1738-1742, 1999.
395. P. Shi, S. P. Shue, and R. K. Agrawal. Robust disturbance attenuation with stability for a class of uncertain singularly perturbed systems. International Journal of Control, 70(6):873-891, 1998.
396. S. D. Shih and R. B. Kellogg. Asymptotic analysis of a singular perturbation problem. SIAM Journal of Mathematical Analysis, 18:1467-1511, 1987.
397. K. Shimizu and Matsubaba. Singular perturbation for the dynamic interaction measure. IEEE Transactions on Automatic Control, AC-30:790-792, 1985.
398. K. R. Shouse and D. G. Taylor. Discrete-time observers for singularly perturbed continuous-time systems. IEEE Transactions on Automatic Control, 40:224-235, 1995.
399. B. Siciliano and W. J. Book. A singular perturbation approach to control of lightweight flexible manipulators. International Journal of Robotic Research, 7(4):79-90, August 1988.
400. R. Silva-Madriz and S. S. Sastry. Input-output description of linear systems with multiple time-scales. International Journal of Control, 40, 1984.
401. R. Silva-Madriz and S. S. Sastry. Feedback systems and multiple time-scales. International Journal of Control, 43, 1986.
402. R. Silva-Madriz and S. S. Sastry. Multiple time-scales for nonlinear systems. Circuits, Systems, Signal Process, 5, 1986.
403. M. G. Singh, editor. Singular Perturbations, volume 7, pages 4425-4443. Pergamon Press, New York, NY, 1987.
404. N. P. Singh and Y. P. Singh. Power system excitation and governor control design via time-scale decomposition. International Journal of Systems Science, 19:1827-1841, 1988.
405. N. P. Singh, Y. P. Singh, and S. I. Ahson. An iterative approach to reduced-order modeling of synchronous machines using singular perturbation. Proceedings of the IEEE, 74:892-893, June 1986.
406. N. P. Singh, Y. P. Singh, and S. I. Ahson. Near-optimal controllers for synchronous machines with prescribed degree of stability via iterative separation of time scales. Proceedings of the IEEE, 74:1466-1468, October 1986.
407. N. P. Singh, Y. P. Singh, and S. I. Ahson. Singular perturbation approach to near-optimum control with a prescribed degree of stability. International Journal of Systems Science, 18:1703-1709, 1987.
408. N. P. Singh, Y. P. Singh, and S. I. Ahson. New design of composite controllers for synchronous machines via separation of time scales. IEE Proceedings: Part D: Control Theory and Applications, 135:182-188, May 1988.
409. S. B. Skaar and C. F. Ruoff, editors. Teleoperation and Robotics in Space. American Institute of Aeronautics and Astronautics, Inc., Washington, DC, 1994.
410. D. R. Smith. The multivariable method in singular perturbation analysis. SIAM Review, 17:221-273, 1975.
411. D. R. Smith. Singular Perturbation Theory: An Introduction with Applications. Cambridge University Press, Cambridge, MA, 1985.
412. D. R. Smith. Decoupling and order reduction via the Riccati transformation. SIAM Review, 29:91-113, March 1987.
413. V. A. Sobolev. Integral manifolds and decomposition of singularly perturbed systems. Systems and Control Letters, 5:169-179, 1984.
414. L. Socha. Experimental stability of singularly perturbed stochastic systems. IEEE Transactions on Automatic Control, 45:576-580, 2000.
415. H. M. Soner. Singular perturbations in manufacturing. SIAM Journal of Control and Optimization, 31:132-146, 1993.
416. M. W. Spong. Modelling and control of elastic joint robots. Transactions of ASME: Journal of Dynamic Systems, Measurement and Control, 109:310-319, 1987.
417. M. W. Spong. On the forced control problem for flexible joint manipulators. IEEE Transactions on Automatic Control, 34:107-111, 1989.
418. M. W. Spong, K. Khorasani, and P. V. Kokotović. A slow manifold approach to feedback control of flexible joint robots. IEEE Journal of Robotics and Automation, RA-3:291-300, 1987.
419. A. M. Steinberg. Stabilization of non-linear singularly perturbed systems with periodic input. International Journal of Control, 43:657-661, 1986.
420. H. Steinrück. Singularly perturbed eigenvalue problems. SIAM Journal of Applied Mathematics, 47:1131-1149, 1987.
421. H. Steinrück. A bifurcation analysis of the one-dimensional steady-state semiconductor device equations. SIAM Journal of Applied Mathematics, 49:1102-1121, 1989.
422. V. Strygin, V. Sobolev, E. Gorelova, and E. Fridman. Integral manifolds of singularly perturbed systems and some of their applications. Differential Equations, 21:1159-1161, 1985.
423. W. C. Su, , Z. Gajić, and X. Shen. The exact slow-fast decomposition of the algebraic Riccati equation of singularly perturbed systems. IEEE Transactions on Automatic Control, AC-37:1456-1459, 1992.
424. N. N. Subbatina. Asymptotic properties of minimax solutions of Isacs-Bellman equations in differential games with fast and slow motions. Journal of Applied Mathematics and Mechanics, 60:883-890, 1996.
425. G. P. Syrcos and P. Sannuti. Near optimum regulator design of singularly perturbed systems via Chandrasekhar equations. International Journal of Control, 39:1083-1102, 1984.
426. P. Szmolyan. A singular perturbation analysis of the transient semiconductor equation. SIAM Journal of Applied Mathematics, 49:1122-1135, August 1989.
427. R. F. Tap, L. G. van Willigenburg, G. van Straten, and E. J. van Henten. Optimal control of green house climate: computation of the influence of fast and slow dynamics. In G. C. Goodwin and R. J. Evans, editors, Proceedings of the 12th Triennial World Congress of the IFAC, Sydney, Australia, July, 18-23, 1993, volume 4, pages 1147-1150. International Federation of Automatic Control, Elsevier Science Ltd, Oxford, UK, 1994.
428. ∞ controllers for a class of nonlinear singular perturbed systems. Automatic, 35:735-739, April 1999.
429. A. Tesfaye and M. Tomizuka. Zeros of discretized continuous systems expressed in the Euler operator - an asymptotic analysis. IEEE Transactions on Automatic Control, 40:743-747, April 1995.
430. A. N. Tikhonov. Systems of differential equations containing small parameters multiplying some of the derivatives. Mathematic Sbovenic, 31(73):575-586, 1952.
431. M. Tran and M. Sawan. Decentralized control of two-time-scale discrete-time systems. International Journal of Systems Science, 15:1295-1300, 1984.
432. M. Tran and M. Sawan. Low-order observer for discrete-time systems with slow and fast modes. International Journal of Systems Science, 15:1283-1288, 1984.
433. M. Tran and M. Sawan. On the well-posedness of discrete-time systems with slow and fast modes. International Journal of Systems Science, 15:1289-1394, 1984.
434. H. Trinh and M. Aldeen. Robust stability of singularly perturbed discrete-delay systems. IEEE Transactions on Automatic Control, 40:1620-1623, 1995.
435. H. D. Tuan and S. Hosoe. A new design for regulator problems for singularly perturbed systems with constraint control. IEEE Transactions on Automatic Control, 42:260-26-1, 1997.
436. H. D. Tuan and S. Hosoe. On a state-space approach to robust control for singularly perturbed systems. International Journal of Control, 66:435-462, 1997.
437. H. D. Tuan and S. Hosoe. Multivariable circle criteria for multiparameter singularly perturbed systems. IEEE Transactions on Automatic Control, 45:720-725, April 2000.
438. P. T. M. van Woerkom. Mathematical models of flexible spacecraft dynamics: a survey of order reduction approaches. Control: Theory and Advanced Technology, 6(4):609-632, December 1990.
439. A. B. Vasil'eva. Asymptotic behavior of solutions to certain problems involving nonlinear ordinary differential equations containing a small parameter multiplying the highest derivatives. Russian Mathematical Surveys, 18:13-84, 1963.
440. A. B. Vasil'eva. The development of the theory of ordinary differential equations with a small parameter multiplying the highest derivatives in the years 1966-1976. Russian Mathematical Surveys, 31:109-131, 1976.
441. A. B. Vasil'eva. On the development of singular perturbation theory at Moscow State University and elsewhere. SIAM Review, 36:440-452, 1994.
442. A. B. Vasil'ova and V. F. Butuzov. Asymptotic Expansions of Solutions of Singularly Perturbed Differential Equations. Izadat. Nauka, Moscow, Russia, 1973.
443. A. B. Vasil'eva, V. F. Butuzov, and L. V. Kalachev. The Boundary Function Method for Singular Perturbation Problems. SIAM Studies in Applied Mathematics, Philadelphia, PA, 1995.
444. A. F. Vaz and E. J. Davison. Modular model reduction for interconnected systems. Automatica, 26:251-261, 1990.
445. V. Veliov. A generalization of the Tikhonov theorem for singularly perturbed differential inclusions. Journal of Dynamical and Control Systems, 3:291-319, 1997.
446. V. Venkatasubramaniam, H. Schattler, and J. Zaborsky. Fast time-varying phasor analysis in the balanced three-phase large electric power system. IEEE Transactions on Automatic Control, 40:1975-1982, 1995.
447. A. Verghese, P. W. Sauer, and M. A. Pai. Synchronous machine block diagram analysis with fast dynamics. Electric Power & Energy Systems, 11:239-247, 1989.
448. F. Verhulst, editor. Asymptotic Analysis: From Theory to Applications, volume 711 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, Germany, 1979.
449. ∞-control of singularly perturbed aircraft model. Optimal Control: Applications & Methods, 15:277-289, 1994.
450. M. Vidyasagar. Robust stabilization of singularly perturbed systems. Systems and Control Letters, 5:413-118, 1985.
451. A. Vigodner. Limits of singularly perturbed control problems with statistical dynamics of fast motions. SIAM Journal of Control and Optimization, 35:1-28, 1997.
452. M. Vishik. Asymptotic Behavior of Solutions of Evolution Equations. Cambridge University Press, Cambrdige, UK, 1992.
453. H. G. Visser and J. Shinar. First-order corrections in optimal feedback control of singularly perturbed nonlinear systems. IEEE Transactions on Automatic Control, AC-31(5):387-393, May 1986.
454. M. S. Wang, T. H. S. Li, and Y. Y Sun. Design of near-optimal observer-based controllers for singularly perturbed discrete systems. JSME International Journal, 39(2):234-241, 1996.
455. Y. Y. Wang and P. M. Frank. Complete decomposition of sub-optimal regulator for singularly perturbed systems. International Journal of Control, 55:49-56, 1992.
456. Y. Y. Wang, P. M. Frank, and N. E. Wu. Near-optimal control of nonstandard singularly perturbed systems. Automatica, 30:277-292, 1994.
457. Y. Y. Wang, S. J. Shi, and Z. J. Zhang. A descriptor-system approach to singular perturbation of linear regulators. IEEE Transactions on Automatic Control, 33:370-373, 1988.
458. W. Wasow. Asymptotic Expansions for Ordinary Differential Equations. Wiley-Interscience, New York, NY, 1965.
459. S. R. Wells. Comments on "zeros of discretized continuous systems expressed in the Euler operator - an asymptotic analysis". IEEE Transactions on Automatic Control, 43:1308-1310, September 1998.
460. H. Xu and K. Mizukami. Infinite-horizon differential games of a singularly perturbed systems: a unified approach. Automatica, 33:273-276, 1997.
461. H. Xu, H. Mukaidani, and K. Mizukami. New method for composite control of singularly perturbed systems. International Journal of Systems Science, 28:161-172, 1997.
462. Y. Xu and T. Kanade, editors. Space Robotics: Dynamics and Control. Kluwer Academic Publishers, Boston, Massachusetts, 1993.
463. G. Yin and Q. Zhang. Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach. springer-Verlag, New York, NY, 1998.
464. E. N. Zharikova and V. A. Sobolev 97. Optimal periodic systems of control with singular perturbations. Automation and Remote Control, 58:1188-12026, July 1997.
465. K. Zhou, J. L. Aravena, G. Gu, and D. Xiong. 2-D model reduction by quasibalanced truncation and singular perturbation. IEEE Transactions on Circuits and Systems-II: Analog and Digital Signal Processing, 41:593-602, 1994.
466. Z. Zhou, M. A. Shayman, and T.-J. Tarn. Singular systems: a new approach in the time domain. IEEE Transactions on Automatic Control, AC-32:42-50, 1987.
467. J. Zhuang and Z. Gajić. Stochastic multimodel strategy with perfect measurements. Control - Theory and Advanced Technology, 7:173-182, 1991.