Robust control and filtering of singular systems

Lecture Notes in Control and Information Sciences

Volumn 332, Issue , 2006, Pages 1-231

  Xu, Shengyuan ^a   Lam, James ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33947680693     PISSN: 01708643     EISSN: None     Source Type: Book Series    
DOI: None     Document Type: Article

References (215)

1. A. Ailon. Controllability of generalized linear time-invariant systems. IEEE Trans. Automat. Control, 32:429-432, 1987.
2. A. Ailon. On the design of output-feedback for finite and infinite pole assignment in singular systems with application to the control problem of constrained robots. Circuit, Syst, Sig. Process., 13:525-544, 1994.
3. B. D. O. Anderson and J. B. Moore. Optimal Filtering. Prentice-Hall, Englewood Cliffs, NJ, 1979.
4. B. D. O. Anderson and J. B. Moore. Linear Optimal Control. Prentice-Hall, NJ: Englewood Cliffs, 1990.
5. B. D. O. Anderson and S. Vongpanitlerd. Network Analysis and Synthesis: A Modern Systems Theory Approach. Upper Saddle River, NJ: Prentice-Hall, 1973.
6. J. D. Aplevich. Implicit Linear Systems. Berlin: Springer-Verlag, 1991.
7. A. Banaszuk, M. Kociecki, and F. L. Lewis. Kalman decomposition for implicit linear systems. IEEE Trans. Automat. Control, 37:1509-1514, 1992.
8. B. R. Barmish. Necessary and sufficient conditions for quadratic stabilizability of an uncertain systems. J. Optim. Theory Appl., 46:399-408, 1985.
9. U. Başer and J. M. Schumacher. The equivalence structure of descriptor representations of systems with possibly inconsistent initial conditions. Linear Algebra Appl., 318:53-77, 2000.
10. T. Beeilen and P. Vandooren. A numerical-method for deadbeat control of generalized state-space systems. Systems & Control Lett., 10:225-233, 1988.
11. D. J. Bender. Lyapunov-like equations and reachability observability gramians for descriptor systems. IEEE Trans. Automat. Control, 32:343-348, 1987.
12. D. J. Bender and A. J. Laub. The linear-quadratic optimal regulator for descriptor systems. IEEE Trans. Automat. Control, 32:672-687, 1987.
13. ∞ error bound. Systems & Control Lett., 12:9-16, 1989.
14. ∞ filtering via LMI. European Journal of Control, 7:2-16, 2001.
15. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan. Linear Matrix Inequalities in System and Control Theory. SIAM Studies in Applied Mathematics. SIAM, Philadelphia, Pennsylvania, 1994.
16. A. Bunse-Gerstner, V. Mehrmann, and N. K. Nichols. Regularization of descriptor systems by derivative and proportional state feedback. SIAM J. Matrix Anal. Appl., 13:46-67, 1992.
17. A. Bunse-Gerstner, V. Mehrmann, and N. K. Nichols. Regularization of descriptor systems by output feedback. IEEE Trans. Automat. Control, 39:1742-1748, 1994.
18. R. Dyers, P. Kunkel, and V. Mehrmann. Regularization of linear descriptor systems with variable coefficients. SIAM J. Control Optim., 35:117-133, 1997.
19. G. D. Byrne and P. R. Ponzi. Differential-algebraic systems, their applications and solutions. Comput. Chem. Engng., 12:377-382, 1988.
20. S. L. Campbell. Singular Systems of Differential Equations. San Francisco: Pitman, 1980.
21. S. L. Campbell. Singular Systems of Differential Equations II. San Francisco: Pitman, 1982.
22. S. L. Campbell. One canonical form for higher-index linear time-varying singular systems. Circuit, Syst, Sig. Process., 2:311-326, 1983.
23. S. L. Campbell and E. Griepentrog. Solvability of general differential algebraic equations. SIAM J. Sci. Comput., 16:257-270, 1995.
24. S.-H. Chen. Robust D-stability analysis for linear discrete-time singular systems with structured parameter uncertainties and delayed perturbations. Proc. Inst. Mech. Eng. Part I-J Syst Control Eng., 217:1-5, 2003.
25. J. H. Chou. Stability robustness of linear state space models with structured perturbations. Syst. Contr. Lett., 15:207-210, 1990.
26. M. A. Christodoulou and C. Isik. Feedback-control for nonlinear singular systems. Int. J. Control, 51:487-494, 1990.
27. M. A. Christodoulou and P. N. Paraskevopoulos. Solvability, controllability, and observability of singular systems. J. Optim. Theory Appl., 45:53-72, 1985.
28. D. L. Chu, H. C. Chan, and D. W. C. Ho. Regularization of singular systems by derivative and proportional output feedback. SIAM J. Matrix Anal. Appl., 19:21-38, 1998.
29. D. L. Chu and D. W. C. Ho. Necessary and sufficient conditions for the output feedback regularization of descriptor systems. IEEE Trans. Automat. Control, 44:405-412, 1999.
30. D. Cobb. Feedback and pole placement in descriptor variable systems. Int. J. Control, 33:1135-1146, 1981.
31. D. Cobb. Descriptor variable systems and optimal state regulation. IEEE Trans. Automat. Control, 28:601-611, 1983.
32. D. Cobb. Controllability, observability, and duality in singular systems. IEEE Trans. Automat. Control, 29:1076-1082, 1984.
33. G. Conte and A. Perdon. Generalized state-space realizations of non-proper rational transfer-functions. Systems & Control Lett., 1:270-276, 1982.
34. L. Dai. Observers for discrete singular systems. IEEE Trans. Automat. Control, 33:187-191, 1988.
35. L. Dai. Filtering and LQG problems for discrete-time stochastic singular systems. IEEE Trans. Automat. Control, 34:110501108, 1989.
36. L. Dai. Singular Control Systems. Berlin: Springer-Verlag, 1989.
37. M. Darouach, M. Zasadzinski, and M. Hayar. Reduced-order observer design for descriptor systems with unknown inputs. IEEE Trans. Automat. Control, 41:1068-1072, 1996.
38. M. Darouach, M. Zasadzinski, and D. Mehdi. State estimation of stochastic singular linear-systems. Int. J. Systems Sci., 24:345-354, 1993.
39. ∞ control for linear systems with Markovian jumping parameters. Control Theory and Advance Technology, 9:457-466, 1993.
40. C. A. Desoer and M. Vidyasagar. Feedback Systems: Input-Output Properties. New York-London: Academic Press, 1975.
41. ∞ control problems. IEEE Trans. Automat. Control, 34:831-847, 1989.
42. V. Dragan and T. Morozan. Stability and robust stabilization to linear stochastic systems described by differential equations with Markov jumping and multiplicative white noise. Stochastic Anal. Appl., 20:33-92, 2002.
43. G. R. Duan and R. J. Patton. Eigenstructure assignment in descriptor systems via state feedback-a new complete parametric approach. Int. J. Systems Sci., 29:167-178, 1998.
44. L. Dugard and E. I. Verriest. Stability and Control of Time-delay Systems. London: Springer-Verlag, 1998.
45. S. H. Esfahani, S. O. R. Moheimani, and I. R. Petersen. LMI approach suboptimal quadratic guaranteed cost control for uncertain time-delay systems. IEE Proc. Control Theory Appl., 145:491-498, 1998.
46. S. H. Esfahani and I. R. Petersen. An LMI approach to the output-feedback guaranteed cost control for uncertain time-delay systems. In Proc. 87th Conf. Decision Control, pages 1358-1363, Tampa, Florida, USA, December, 1998.
47. C.-H. Fang and F.-R. Chang. A strongly observable and controllable realization of descriptor systems. Control Theory Adv. Tech., 6:133-141, 1990.
48. C.-H. Fang and F.-R. Chang. Analysis of stability robustness for generalized state-space systems with structured perturbations. Systems & Control Lett., 21:109-114, 1993.
49. C.-H. Fang, L. Lee, and F.-R. Chang. Robust control analysis and design for discrete-time singular systems. Automatica, 30:1741-1750, 1994.
50. X. Feng, K. A. Loparo, Y. Ji, and H. J. Chizeck. Stochastic stability properties of jump linear systems. IEEE Trans. Automat. Control, 37:38-53, 1992.
51. L. R. Fletcher. Regularizability of descriptor systems. Int. J. Systems Sci., 17:843-847, 1986.
52. ∞-control of linear state-delay descriptor systems: an LMI approach. Linear Algebra Appl., 351/352:271-302, 2002.
53. ∞ optimal estimation and its interconnection to loop transfer recovery. Systems & Control Lett., 17:29-36, 1991.
54. M. Fukuda and M. Kojima. Branch-and-cut algorithms for the bilinear matrix inequality eigenvalue problem. Comput. Optim. Appl., 19:79-105, 2001.
55. ∞ control. Int. J. Robust & Nonlinear Control, 4:421-448, 1994.
56. Z. Gao. PD observer parametrization design for descriptor systems. J. Franklin Inst., 342:551-564, 2005.
57. G. Garcia, J. Bernussou, and D. Arzelier. Robust stabilization of discrete-time linear systems with norm-bounded time-varying uncertainty. Systems & Control Lett., 22:327-339, 1994.
58. T. Geerts. Solvability conditions, consistency, and weak consistency for linear differential-algebraic equations and time-invariant singular systems: The general case. Linear Algebra Appl., 181:111-130, 1993.
59. T. Geerts. Stability concepts for general continuous-time implicit systems-definitions, hautus tests and lyapunov criteria. Int. J. Systems Sci., 26:481-498, 1995.
60. ∞ filtering of stationary continuous-time linear systems with stochastic uncertainties. IEEE Trans. Automat. Control, 46:1788-1793, 2001.
61. H. Glusingluerssen. Feedback canonical form for singular systems. Int. J. Control, 52:347-376, 1990.
62. H. Glusingluerssen and D. Hinrichsen. A Jordan control canonical form for singular systems. Int. J. Control, 48:1769-1785, 1988.
63. M. S. Goodwin. Exact pole assignment with regularity by output feedback in descriptor systems. II. Int. J. Control, 62:413-441, 1995.
64. M. S. Goodwin and L. R. Fletcher. Exact pole assignment with regularity by output feedback in descriptor systems. I. Int. J. Control, 62:379-411, 1995.
65. ∞ model reduction via linear matrix inequalities: continuous- and discrete-time cases. Systems & Control Lett., 26:321-333,1995.
66. ∞ filtering via linear matrix inequalities. IEEE Trans. Aerospace and Electronic Systems, 33:1326-1338, 1997.
67. J. Grimm. Realization and canonicity for implicit systems. SIAM J. Control Optim., 26:1331-1347, 1988.
68. Z.-H. Guan and J. Lam. Robust stability of composite singular and impulsive interval uncertain dynamic systems with time delay. 32:1297-1307, 2001.
69. ∞ control for descriptor systems with non-linear uncertainties. Int. J. Control, 76:1254-1262, 2003.
70. W. M. Haddad and D. S. Bernstein. Robust stabilization with positive real uncertainty: beyond the small gain theorem. Systems & Control Lett., 17:191-208, 1991.
71. W. M. Haddad and D. S. Bernstein. Explicit construction of quadratic Lyapunov functions for the small gain, positivity, circle, and Popov theorems and their application to robust stability, part II: discrete-time theory. Int. J. Robust & Nonlinear Control, 4:249-265, 1994.
72. J. K. Hale. Theory of Functional Differential Equations. New York: Springer-Verlag, 1977.
73. G. Hayton, P. Fretwell, and A. Pugh. Fundamental equivalence of generalized state-space systems. IEEE Trans. Automat. Control, 31:431-439, 1986.
74. U. Helmke and M. A. Shayman. A canonical form for. controllable singular systems. Systems & Control Lett., 12:111-122, 1989.
75. H. Hemami and B. F. Wyman. Modeling and control of constrained dynamic systems with application to biped locomotion in the frontal plane. IEEE Trans. Automat. Control, 24:526-535, 1979.
76. D. Hinrichsen, W. Manthey, and U. Helmke. Minimal partial realization by descriptor systems. Linear Algebra Appl., 326:45-84, 2001.
77. D. Hinrichsen and J. Ohalloran. A complete characterization of orbit closures of controllable singular systems under restricted system equivalence. SIAM J. Control Optim., 28:602-623, 1990.
78. M. Hou. Controllability and elimination of impulsive modes in descriptor systems. IEEE Trans. Automat. Control, 49:1723-1727, 2004.
79. M. Hou and P. C. Muller. Observer design for descriptor systems. IEEE Trans. Automat. Control, 44:164-169, 1999.
80. K.-L. Hsiung and L. Lee. Lyapunov inequality and bounded real lemma for discrete-time descriptor systems. IEE Proc.-Control Theory Appl., 146:327-331, 1999.
81. ∞ control for uncertain linear time-invariant descriptor systems. IEE Proc.-Control Theory Appl., 147:648-654, 2000.
82. J. Y. Ishihara and M. H. Terra. On the Lyapunov theorem for singular systems. IEEE Trans. Automat. Control, 47:1926-1930, 2002.
83. 2 optimal controllers for descriptor systems. Automatica, 39:391-402, 2003.
84. ∞ control problems: LMI existence conditions and state space formulas. Automatica, 30:1307-1317, 1994.
85. Y. Ji and H. J. Chizeck. Jump linear quadratic Gaussian control: steady-state solution and testable conditions. Control Theory Adv. Tech., 6:289-319, 1990.
86. ∞ filtering for polytopic uncertain systems via convex optimisation. IEE Proc.-Control Theory Appl., 148:55-59, 2001.
87. T. Kaczorek. Stabilization of linear descriptor systems by state-feedback controllers. Appl. Math. Comput. Sci., 6:27-32, 1996.
88. ∞ control theory. IEEE Trans. Automat. Control, 35:356-361, 1990.
89. D. Koenig and S. Mammar. Design of proportional-integral observer for unknown input descriptor systems. IEEE Trans. Automat. Control, 47:2057-2062, 2002.
90. V. B. Kolmanovskii and A. D. Myshkis. Applied Theory of Functional Differential Equations. Dordrecht: Kluwer Academic Publishers, 1992.
91. F. N. Koumboulis and P. N. Paraskevopoulos. On the pole assignment of generalized state-space systems via state feedback. IEE Proc.-Control Theory Appl., 139:106-108, 1992.
92. F. N. Koumboulisa and P. N. Paraskevopoulos. On the generic controllability of continuous generalized state-space systems. Automatica, 29:527-530, 1993.
93. M. Krstić, I. Kanellakopoulos, and P. V. Kokotovic. Nonlinear and Adaptive Control Design. New York: John Wiley Sons Inc., 1995.
94. M. Kuijper and J. M. Schumacher. Realization of autoregressive equations in pencil and descriptor form. SIAM J. Control Optim., 28:1162-1189, 1990.
95. A. Kumar and P. Daoutidis. Feedback control of nonlinear differential-algebraic equation systems. AIChE Journal, 41:619-636, 1995.
96. A. Kumar and P. Daoutidis. State-space realizations of linear differential-algebraic-equation systems with control-dependent state space. IEEE Trans. Automat. Control, 41:269-274, 1996.
97. A. Kumar and P. Daoutidis. Control of Nonlinear Differential Algebraic Equation Systems. Boca Raton : Chapman & Hall/CRC, 1999.
98. P. Kunkel and V. Mehrmann. The linear quadratic optimal control problem for linear descriptor systems with variable coefficients. Maths. Contr. Sig. Sys., 10:247-264, 1997.
99. Y.-C. Kuo, W.-W. Lin, and S.-F. Xu. Regularization of linear discrete-time periodic descriptor systems by derivative and proportional state feedback. SIAM J. Matrix Anal. Appl., 25:1046-1073, 2003.
100. G. A. Kurina and R. März. On linear-quadratic optimal control problems for time-varying descriptor systems. SIAM J. Control Optim., 42:2062-2077, 2004.
101. P. Lancaster and M. Tismenetsky. The Theory of Matrices. 2nd edition. New York: Academic Press, 1985.
102. G. Lebret and J. J. Loiseau. Proportional and proportional-derivative canonical-forms for descriptor systems with outputs. Automatica, 30:847-864, 1994.
103. ∞ controllers for state delayed systems. IEEE Trans. Automat. Control, 39:159-162, 1994.
104. L. Lee and J. L. Chen. Strictly positive real lemma and absolute stability for discrete-time descriptor systems. IEEE Trans. Circuits Syst. I, 50:788-794, 2003.
105. L. Lee and C.-H. Fang. An improved bound for stability robustness of uncertain generalized state-space systems. In Proc. American Control Conference, pages 240-241, Baltimore, Maryland, 1994.
106. L. Lee, C.-H. Fang, and J.-G. Hsieh. Exact unidirectional perturbation bounds for robustness of uncertain generalized state-space systems: continuous-time cases. Automatica, 33:1923-1927, 1997.
107. F. L. Lewis. Descriptor systems: Decomposition into forward and backward subsystems. IEEE Trans. Automat. Control, 29:167-170, 1984.
108. F. L. Lewis. A survey of linear singular systems. Circuits, Syst. Signal Processing, 5:3-36, 1986.
109. X. Li and C. E. de Souza. Criteria for robust stability and stabilization of uncertain linear systems with state-delay. Automatica, 33:1657-1662, 1997.
110. X. Li and C. E. de Souza. Delay-dependent robust stability and stabilization of uncertain linear delay systems: a linear matrix inequality approach. IEEE Trans. Automat. Control, 42:1144-1148, 1997.
111. C. Lin, J. Wang, and C. B. Soh. Maximum bounds for robust stability of linear uncertain descriptor systems with structured perturbations. Int. J. Systems Sci., 34:463-467, 2003.
112. C. Lin, J. Wang, D. Wang, and C. B. Soh. Robustness of uncertain descriptor systems. Systems & Control Lett., 31:129-138, 1997.
113. C. Lin, J. Wang, G.-H. Yang, and J. Lam. Robust stabilization via state feedback for descriptor systems with uncertainties in the derivative matrix. Int. J. Control, 73:407-415, 2000.
114. C. Lin, J. Wang, G.-H. Yang, and C. B. Soh. Robust C-controllability and/or C-observability for uncertain descriptor systems with interval perturbations in all matrices. IEEE Trans. Automat. Control, 44:1768-1773, 1999.
115. C. Lin, Q.-G. Wang, and T. H. Lee. Robust normalization and stabilization of uncertain descriptor systems with norm-bounded perturbations. IEEE Trans. Automat. Control, 50:515-520, 2005.
116. J. L. Lin and S. J. Chen. LFT approach to robust D-stability bounds of uncertain linear singular systems. IEE Proc.-Control Theory Appl., 145:127-134, 1998.
117. W. Q. Liu, K. L. Teo, and W. Y. Yan. Optimal simultaneous stabilization of descriptor systems via output feedback. Int. J. Control, 64:595-613, 1996.
118. X. Liu. Local disturbance decoupling of nonlinear singular systems. Int. J. Control, 70:685-702, 1998.
119. X. Liu and S. Čelikovský. Feedback control of affine nonlinear singular control systems. Int. J. Control, 68:753-774, 1997.
120. A. Luenberger, D. G.and Arbel. Singular dynamic Leontief systems. Econometrica, 45:991-995, 1977.
121. D. G. Luenberger. Dynamic equations in descriptor form. IEEE Trans. Automat. Control, 22:312-321, 1977.
122. D. G. Luenberger. Time-invariant descriptor systems. Automatica, 14:473-480, 1978.
123. M. Mariton. Jump Linear Systems in Automatic Control. New York : Marcel Dekker, 1990.
124. B. Marx, D. Koenig, and D. Georges. Robust fault-tolerant control for descriptor systems. IEEE Trans. Automat. Control, 49:1869-1875, 2004.
125. ∞ control for descriptor systems: a matrix inequalities approach. Automatica, 33:669-673, 1997.
126. J. K. Mills and A. A. Goldenberg. Force and position control of manipulators during constrained motion tasks. IEEE Trans. Robot. Automat., 5:30-46, 1989.
127. N. Minamide, Y. Fujisaki, and A. Shimizu. A parametrization of all observers for descriptor systems. Int. J. Control, 66:767-777, 1997.
128. P. Misra and R. V. Patel. Computation of minimal-order realizations of generalized state-space systems. Circuit, Syst, Sig. Process., 8:49-70, 1989.
129. P. C. Muller and M. Hou. On the observer design for descriptor systems. IEEE Trans. Automat. Control, 38:1666-1671, 1993.
130. ∞ setting. IEEE Trans. Automat. Control, 36:152-166, 1991.
131. R. W. Newcomb. The semistate description of nonlinear time-variable circuits. IEEE Trans. Circuits Syst., 28:62-71, 1981.
132. R. W. Newcomb and B. Dziurla. Some circuits and systems applications of semistate theory. Circuit, Syst, Sig. Process., 8:235-260, 1989.
133. N. K. Nichols. On the stability radius of a generalized state-space system. Linear Algebra Appl., 188, 1993.
134. S.-I. Niculescu. Delay Effects on Stability : A Robust Control Approach. Berlin : Springer, 2001.
135. R. Nikoukhah, S. L. Campbell, and F. Delebecque. Kalman filtering for general discrete-time linear systems. IEEE Trans. Automat. Control, 44:1829-1839, 1999.
136. K. Ozcaldiran and F. L. Lewis. On the regularizability of singular systems. IEEE Trans. Automat. Control, 35:1156-1160, 1990.
137. L. Pandolfi. Controllability and stabilization for linear systems of algebraic and differential equations. J. Optim. Theory Appl., 30:601-620, 1980.
138. L. Pandolfi. On the regulator problem for linear degenerate control systems. J. Optim. Theory Appl., 33:241-254, 1981.
139. S. Pang, J. Huang, and Y. Bai. Robust output regulation of singular nonlinear systems via a nonlinear internal model. IEEE Trans. Automat. Control, 50:222-228, 2005.
140. P. N. Paraskevopoulos and F. N. Koumboulis. Unifying approach to observers for regular and singular systems. IEE Proc.-Control Theory Appl., 138:561-572, 1991.
141. P. N. Paraskevopoulos and F. N. Koumboulis. Observers for singular systems. IEEE Trans. Automat. Control, 37:1211-1215, 1992.
142. ∞ filtering via convex optimization. Int. J. Control, 66:15-22, 1997.
143. I. R. Petersen and D. C. McFarlane. Optimal guaranteed cost control and filtering for uncertain linear systems. IEEE Trans. Automat. Control, 39:1971-1977, 1994.
144. L. Qiu and E. J. Davison. The stability robustness of generalized eigenvalues. IEEE Trans. Automat. Control, 37:886-891, 1992.
145. J. Rodriguez and D. Sweet. A characterization of semistate systems. Circuit, Syst, Sig. Process., 5:125-137, 1986.
146. B. Scott. Power system dynamic response calculations. Proc. IEEE, 67:219-247, 1979.
147. ∞-optimal estimation: a tutorial. In Proc. 31st IEEE Conf. Decision and Control, pages 2278-2286, Tucson, Arizona, USA, December, 1992.
148. A. A. Shcheglova and V. F. Chistyakov. Stability of linear differential-algebraic systems. Differ. Equ., 40:50-62, 2004.
149. P. Shi, E. K. Boukas, and R. K. Agarwal. Kalman filtering for continuous-time uncertain systems with Markovian jumping parameters. IEEE Trans. Automat. Control, 44:1592-1597, 1999.
150. D. N. Shields. Observer design for discrete nonlinear descriptor systems. Int. J. Systems Sci., 27:1033-1041, 1996.
151. S. Singh and R.-W. Liu. Existence of state equation representation of linear large-scale dynamical systems. IEEE Trans. Circuits Syst., 20:239-246, 1973.
152. B. L. Stevens and F. L. Lewis. Aircraft Modeling, Dynamics and Control. New York: Wiley, 1991.
153. W. Sun, P. P. Khargonekar, and D. Shim. Solution to the positive real control problem for linear time-invariant systems. IEEE Trans. Automat. Control, 39:2034-2046, 1994.
154. V. L. Syrmos, P. Misra, and R. Aripirala. On the discrete generalized Lyapunov equation. Automatica, 31:297-301, 1995.
155. 2 output feedback control for descriptor systems. Systems & Control Lett., 34:841-850, 1988.
156. ∞ filters. Int. J. Control, 64:1129-1149, 1996.
157. ∞, control for descriptor systems-a J-spectral factorization appraoch. In Proc. 33rd IEEE Conf. Decision and Control, pages 2251-2256, Lake Buena Vista, FL, USA, 1994.
158. K. Takaba, N. Morihira, and T. Katayama. A generalized Lyapunov theorem for descriptor system. Systems & Control Lett., 24:49-51, 1995.
159. A. Tornambè. A simple procedure for the stabilization of a class of uncontrollable generalized systems. IEEE Trans. Automat. Control, 41:603-607, 1996.
160. H. D. Tuan and P. Apkarian. Low nonconvexity-rank bilinear matrix inequalities: algorithms and applications in robust controller and structure designs. IEEE Trans. Automat. Control, 45:2111-2117, 2000.
161. H. D. Tuan, P. Apkarian, and Y. Nakashima. A new lagrangian dual global optimization algorithm for solving bilinear matrix inequalities. Int. J. Robust & Nonlinear Control, 10:561-578, 2000.
162. D. Vafiadis and N. Karcanias. Canonical forms for descriptor systems under restricted system equivalence. Automatica, 33:955-958, 1997.
163. D. Vafiadis and N. Karcanias. Block decoupling and pole assignment of singular systems: frequency domain approach. Int. J. Control, 76:185-192, 2003.
164. A. Varga. On stabilization methods of descriptor systems. Systems & Control Lett., 24:133-138, 1995.
165. G. C. Verghese, B. C. Lévy, and T. Kailath. A generalized state-space for singular systems. IEEE Trans. Automat. Control, 26:811-831, 1981.
166. E. I. Verriest and A. F. Ivanov. Robust stability of delay-difference equations. In Proc. 34th IEEE Conf. Decision and Control, pages 386-391, New Orleans, LA, December, 1995.
167. M. Vidyasagar. Nonlinear Systems Analysis. Prentice-Hall, Englewood Cliffs, New Jersey, 1993.
168. C. J. Wang. On linear quadratic optimal control of linear time-varying singular systems. Int. J. Systems Sci., 35:903-906, 2004.
169. D. Wang and C. B. Soh. On regularizing singular systems by decentralized output feedback. IEEE Trans. Automat. Control, 44:148-152, 1999.
170. ∞ control for descriptor systems. IEE Proc.-Control Theory Appl., 145:316-322, 1998.
171. Y.-Y. Wang, S.-J. Shi, and Z.-J. Zhang. Pole placement and compensator design of generalized systems. Systems & Control Lett., 8:205-209, 1987.
172. G. Xie and L. Wang. Controllability of linear descriptor systems. IEEE Trans. Circuits Syst. I, 50:455-460, 2003.
173. ∞, control for linear systems with normbounded time-varying uncertainty. IEEE Trans. Automat. Control, 37:1188-1191, 1992.
174. L. Xie and Y. C. Soh. Guaranteed cost control of uncertain discrete-time systems. Control Theory Adv. Tech., 10:1235-1251, 1995.
175. L. Xie and Y. C. Soh. Positive real control for uncertain linear time-invariant systems. Systems & Control Lett., 24:265-271, 1995.
176. ∞ model reduction for discrete-time singular systems. Systems & Control Lett., 48:121-133, 2003.
177. S. Xu and J. Lam. Robust stability for uncertain discrete singular systems with state delay. Asian Journal of Control, 5:399-405, 2003.
178. S. Xu and J. Lam. New positive realness conditions for uncertain discrete descriptor systems: analysis and synthesis. IEEE Trans. Circuits Syst. I, 51:1897-1905, 2004.
179. S. Xu and J. Lam. Robust stability and stabilization of discrete singular systems: an equivalent characterization. IEEE Trans. Automat. Control, 49, 2004.
180. ∞ model reduction for singular systems: continuous-time case. IEE Proc.-Control Theory Appl., 150:637-641, 2003.
181. ∞, and positive real control for linear neutral delay systems. IEEE Trans. Automat. Control, 46:1321-1326, 2001.
182. S. Xu, J. Lam, and C. Yang. Quadratic stability and stabilization of uncertain linear discrete-time systems with state delay. Systems & Control Lett., 43:77-84, 2001.
183. ∞, control for discrete singular systems with state delay and parameter uncertainty. Dynamics of Continuous, Discrete and Impulsive Systems, Series B: Applications and Algorithms, 9:539-554, 2002.
184. ∞ control for uncertain singular systems with state delay. Int. J. Robust & Nonlinear Control, 13:1213-1223, 2003.
185. S. Xu, J. Lam, C. Yang, and E. I. Verriest. An LMI approach to guaranteed cost control for uncertain linear neutral delay systems. Int. J. Robust & Nonlinear Control, 13:35-53, 2003.
186. S. Xu, J. Lam, and L. Zhang. Robust D-stability analysis for uncertain discrete singular systems with state delay. IEEE Trans. Circuits Syst. I, 49:551-555, 2002.
187. ∞, filtering for singular systems. IEEE Trans. Automat. Control, 48:2217-2222, 2003.
188. 8. Xu, P. Van Dooren, R. Stefan, and J. Lam. Robust stability and stabilization for singular systems with state delay and parameter uncertainty. IEEE Trans. Automat. Control, 47:1122-1128, 2002.
189. S. Xu and C. Yang. Stabilization of discrete-time singular systems: a matrix inequalities approach. Automatica, 35:1613-1617, 1999.
190. S. Xu and C. Yang. An algebraic approach to the robust stability analysis and robust stabilization of uncertain singular systems. Int. J. Systems Sci., 31:55-61, 2000.
191. ∞, state feedback control for discrete singular systems. IEEE Trans. Automat. Control, 45:1405-1409, 2000.
192. S. Xu, C. Yang, Y. Niu, and J. Lam. Robust stabilization for uncertain discrete singular systems. Automatica, 37:769-774, 2001.
193. ∞-norm estimation. IEEE Trans. Automat. Control, 37:828-831, 1992.
194. C. W. Yang and H. L. Tan. Observer design for singular systems with unknown inputs. Int. J. Control, 49:1937-1946, 1989.
195. E. L. Yip and R. F. Sincovec. Solvability, controllability and observability of continuous descriptor systems. IEEE Trans. Automat. Control, 26:702-707, 1981.
196. L. Yu and J. Chu. An LMI approach to guaranteed cost control of linear uncertain time-delay systems. Automatica, 35:1155-1159, 1999.
197. R. Yu and D. Wang. Structural properties and poles assignability of LTI singular systems under output feedback. Automatica, 39:685-692, 2003.
198. ∞ filter design of uncertain descriptor systems with discrete and distributed delays. IEEE Trans. Signal Processing, 52:3200-3212, 2004.
199. ∞ controller design for uncertain descriptor systems with distributed delays. Comput. Math. Appl., 47:1041-1055, 2004.
200. G. Zhang, Q. L. Zhang, T. Chen, and Y. Lin. On Lyapunov theorems for descriptor systems. Discrete Contin. Dyn. Syst.-Ser. B, 10:709-725, 2003.
201. L. Zhang and B. Huang. Robust model predictive control of singular systems. IEEE Trans. Automat. Control, 49:1000-1011, 2004.
202. L. Zhang, B. Huang, and J. Lam. Robust guaranteed cost control of descriptor systems. Discrete Contin. Dyn. Syst.-Ser. B, 10:633-646, 2003.
203. L. Zhang, J. Lam, and S. Xu. On positive realness of descriptor systems. IEEE Trans. Circuits Syst. I, 49:401-407, 2002.
204. L. Zhang, J. Lam, and Q. L. Zhang. Lyapunov and Riccati equations of discrete-time descriptor systems. IEEE Trans. Automat. Control, 44:2134-2139, 1999.
205. L. Zhang, J. Lam, and Q. L. Zhang. Optimal model reduction of discrete-time descriptor systems. Int. J. Systems Sci., 32:575-583, 2001.
206. Q. L. Zhang, J. Lam, and L. Zhang. On analyzing the stability of discrete descriptor systems via generalized Lyapunov equations. In Multi-objective Programming and Goal Programming, Adv. Soft Comput., pages 295-300. Springer, Berlin, 2003.
207. Q. L. Zhang, W. Q. Liu, and D. Hill. A Lyapunov approach to analysis of discrete singular systems. Systems & Control Lett., 45:237-247, 2002.
208. S. Y. Zhang. Pole placement for singular systems. Systems & Control Lett., 12:339-342, 1989.
209. K. Zhou, J. C. Doyle, and K. Glover. Robust and Optimal Control. Prentice-Hall, Upper Saddle River, NJ., 1996.
210. K. Zhou and P. P. Khargonekar. Robust stabilization of linear systems with norm-bounded time-varying uncertainty. Systems & Control Lett., 10:17-20, 1988.
211. S. Zhou and J. Lam. Robust stabilization of delayed singular systems with linear fractional parametric uncertainties. Circuit, Syst, Sig. Process., 22:579-588, 2003.
212. Z. Zhou, M. A. Shayman, and T.-J. Tarn. Singular systems: a new approach in the time domain. IEEE Trans. Automat. Control, 32:42-50, 1987.
213. J. Zhu, S. Ma, and Z. Cheng. Singular LQ problem for nonregular descriptor systems. IEEE Trans. Automat. Control, 47:1128-1133, 2002.
214. G. Zimmer and J. Meier. On observing nonlinear descriptor systems. Systems & Control Lett., 32:43-48, 1997.
215. Y. Zou and C. Yang. Formulas for the distance between controllable and uncontrollable linear-systems. Systems & Control Lett., 21:173-180, 1993.