Linear control theory: Structure, robustness, and optimization

Linear Control Theory: Structure, Robustness, and Optimization

Volumn , Issue , 2009, Pages 1-911

  Bhattacharyya, Shankar P ^a   Datta, Aniruddha ^a   Keel, L H ^b  

^a TEXAS A AND M UNIVERSITY   (United States)

^b TENNESSEE STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85056035779     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Book

References (216)

1. Aguirre, G., Chapellat, H. and Bhattacharyya, S. P. Stability margins for discrete - time uncertain systems. In Proceedings of the 1989 IEEE Conference on Decision and Control (Tampa, FL, December 1989).
2. Ahmad, S. S. and Keel, L. H. Robust lead - lag compensation for uncertain linear systems. In Proceedings of the 1992 IEEE Symposium on Circuits and Systems (San Diego, CA, 1992), pp. 2716–2719.
3. Ahmad, S. S., Keel, L. H. and Bhattacharyya, S. P. Computer aided robust control design for interval control system. In Proceedings of the IEEE Symposimum on Computer Aided Control System Design (Napa, CA, 1992), pp. 82 – 89.
4. Ahmad, S. S., Keel, L. H. and Bhattacharyya, S. P. Robust PID control and lead - lag compensator for linear interval systems. In Robustness of Dynamic Systems with Parameter Uncertainties, M. Mansour, S. Balemi, and W. Truöl, Eds. Birkhäuser, Berlin, 1992, pp. 251 - 260.
5. Aizerman, M. A. and Gantmacher, F. R. Absolute Stability of Regulator Systems. Holden - Day, San Francisco, CA, 1964. Russian Edition, 1963.
6. Anderson, B. D. O., Kraus, F., Mansour, M. and Dasgupta, S. Easily testable sufficient conditions for the robust stability of systems with multiaffine parameter dependence. In Robustness of Dynamic Systems with Parameter Uncertainties, M. Mansour, S. Balemi, and W. Truöl, Eds. Birkhäuser, Berlin, 1992, pp. 81 – 92.
7. Åström, K. J. and Hägglund, T. Automatic tuning of simple regulators with specifications on phase and amplitude margins. Automatica 20 (1984), 645 – 651.
8. Åström, K. J. and Hägglund, T. PID Controllers: Theory, Design, and Tuning. Instrument Society of America, Research Triangle Park, NC, 1995.
9. Atherton, D. P. and Majhi, S. Limitations of PID controllers. In Proceedings of the 1999 American Control Conference (San Diego, GA, June 1999).
10. Barmish, B. R. Invariance of strict Hurwitz property of polynomials with perturbed coefficients. IEEE Transactions on Automatic Control AC - 29, 10 (1984), 935 – 936.
11. Barmish, B. R. New tools for robustness analysis. In Proceedings of the 27th IEEE Conference on Decision and Control (Austin, TX, December 1988).
12. Barmish, B. R. A generalization of Kharitonov’s four polynomial concept for robust stability problems with linearly dependent coefficient perturbations. IEEE Transactions on Automatic Control 34, 2 (February 1989), 157 – 165.
13. Barmish, B. R., Hollot, C. V., Kraus, F. J. and Tempo, R. Extreme point results for robust stabilization of interval plants with first order compensators. IEEE Transactions on Automatic Control 37, 6 (June 1992), 707 – 714.
14. Barmish, B. R., Khargonekar, P. P., Shi, Z. and Tempo, R. Robustness margin need not be a continuous function of the problem data. Systems & Control Letters 15 (1989), 371 – 381.
15. Bartlett, A. C. Nyquist, Bode, and Nichols plots of uncertain systes. In Proceedings of the 1990 American Control Conference (San Diego, CA, 1990).
16. Bartlett, A. C. Vertex results for the steady state analysis of uncertain systems. IEEE Transactions on Automatic Control 37, 11 (November 1992), 1758 – 1762.
17. Bartlett, A. C., Hollot, C. V. and Lin, H. Root location of an entire polytope of polynomials: It suffices to check the edges. Mathematics of Controls, Signals and Systems 1 (1988), 61 – 71.
18. Bartlett, A. C., Tesi, A. and Vicino, A. Frequency response of uncertain systems with interval plants. IEEE Transactions on Automatic Control 38, 6 (June 1993), 929 – 933.
19. Basu, S. On boundary implications of stability and positivity properties of multidimensional systems. IEEE Proceedings 78, 4 (1990), 614 – 626.
20. Bellman, R. and Majhi, S. Differential - Difference Equations. Academic Press, London, UK, 1963.
21. Bhattacharyya, S. P. Output regulation with bounded energy. IEEE Transactions on Automatic Control AC - 18, 4 (1973), 381 – 383.
22. Bhattacharyya, S. P. Robust parametric stability: The role of the CB segments. In Control of Uncertain Dynamic Systems, S. P. Bhattacharyya and L. H. Keel, Eds. CRC Press, Littleton, MA, September 1991.
23. Bhattacharyya, S. P. Vertex results in robust stability. Tech. rep., TCSP Report, Texas A&M University, April 1991.
24. Bhattacharyya, S. P., Chapellat, H. and Keel, L. H. Robust Control: The Parametric Approach. Prentice Hall PTR, Upper Saddle River, NJ, 1995.
25. Bhattacharyya, S. P. and Keel, L. H., Eds. Control of Uncertain Dynamic Systems. CRC Press, Littleton, MA, 1991.
26. Bhattacharyya, S. P. and Keel, L. H. Robust stability and control of linear and multilinear interval systems. In Control and Dynamic Systems, C. T. Leondes, Ed., vol. 51. Academic Press, New York, NY, 1992, pp. 31 – 78.
27. Bhattacharyya, S. P., Keel, L. H. and Howze, J. W. Stabilization of linear systems with fixed order controllers. Linear Algebra and Its Applications 98 (1988), 57 – 76.
28. Bhattacharyya, S. P. and Pearson, J. B. On the linear servomechanism problem. International Journal of Control 12, 5 (1970), 795 – 806.
29. Bhattacharyya, S. P. and Pearson, J. B. On error systems and the servomechanism problem. International Journal of Control 15, 6 (1972), 1041 – 1062.
30. Bhattacharyya, S. P., Pearson, J. B. and Wonham, W. M. On zeroing the output of a linear system. Information and Control 2 (1972), 135 – 142.
31. Bialas, S. A necessary and sufficient condition for stability of interval matrices. International Journal of Control 37 (1983), 717 – 722.
32. Bialas, S. A necessary and sufficient condition for the stability of convex combinations of stable polynomials and matrices. Bulletin of Polish Academy of Science 39, 9 - 10 (1985), 473 – 480.
33. Biernacki, R. M., Hwang, H. and Bhattacharyya, S. P. Robust stabilization of plants subject to structured real parameter perturbations. IEEE Transactions on Automatic Control AC - 32, 6 (June 1987), 495 – 506.
34. Bose, N. K. A system - theoretic approach to stability of sets of polynomials. Contemporary Mathematics 47 (1985), 25 – 34.
35. Bose, N. K. Robust multivariable scattering Hurwitz interval polynomials. Linear Algebra and Its Application 98 (1988), 123 – 136.
36. Bose, N. K. Test of Hurwitz and Schur properties of convex combination of complex polynomials. IEEE Transactions on Automatic Control 36, 9 (1989), 1245 – 1247.
37. Bose, N. K. Digital Filters. Elsevier - Science North - Holland, Krieger Publishing Co., New York, 1993.
38. Bose, N. K. Argument conditions for Hurwitz and Schur polynomials from network theory. IEEE Transactions on Automatic Control 39, 2 (February 1994), 345 – 346.
39. Bose, N. K. and Delansky, J. F. Boundary implications for interval positive rational functions. IEEE Transactions on Circuits and Systems CAS - 36 (1989), 454 – 458.
40. Bose, N. K. and Shi, Y. Q. Network realizability theory approach to stability of complex polynomials. IEEE Transactions on Automatic Control 34, 2 (1987), 216 – 218.
41. Bose, N. K. and Shi, Y. Q. A simple general proof of Kharitonov’s general stability criterion. IEEE Transactions on Circuits and Systems CAS - 34 (1987), 1233 – 1237.
42. Brasch, F. M. and Pearson, J. B. Pole placement using dynamic compensator. IEEE Transactions on Automatic Control AC - 15, 1 (February 1970), 34 – 43.
43. Chang, B. C. and Pearson, J. B. Optimal disturbance reduction in linear multivariable systems. IEEE Transactions on Automatic Control AC - 29 (October 1984), 880 – 887.
44. Chapellat, H. and Bhattacharyya, S. P. Calculation of maximal stability domains using an optimal property of Kharitonov polynomials. In Analysis and Optimization of Systems, Lecture Notes in Control and Information Sciences. Springer - Verlag, 1988, pp. 22 – 31.
45. Chapellat, H. and Bhattacharyya, S. P. An alternative proof of Kharitonov’s theorem. IEEE Transactions on Automatic Control AC - 34, 4 (April 1989), 448 – 450.
46. Chapellat, H. and Bhattacharyya, S. P. A generalization of Kharitonov’s theorem: Robust stability of interval plants. IEEE Transactions on Automatic Control AC - 34, 3 (March 1989), 306 – 311.
47. Chapellat, H. and Bhattacharyya, S. P. Robust stability and stabilization of interval plants. In Robustness in Identification and Control, M. Milanese, R. Tempo, and A. Vicino, Eds. Plemum, New York, 1989, pp. 207 – 229.
48. Chapellat, H., Bhattacharyya, S. P. and Keel, L. H. Stability margin for Hurwitz polynomials. In Proceedings of the 27th IEEE Conference on Decision and Control (Austin, TX, December 1988), pp. 1392 – 1398.
49. Chapellat, H., Dahleh, M. and Bhattacharyya, S. P. Robust stability under structured and unstructured perturbations. IEEE Transactions on Automatic Control AC - 35, 10 (October 1990), 1100 – 1108.
50. Chapellat, H., Dahleh, M. and Bhattacharyya, S. P. On robust nonlinear stability of interval control systems. IEEE Transactions on Automatic Control AC - 36, 1 (January 1991), 59 – 67.
51. Chapellat, H., Mansour, M. and Bhattacharyya, S. P. Elementary proofs of some classical stability criteria. IEEE Transactions on Education 33, 3 (1990), 232 – 239.
52. Choksy, N. H. Time - lag systems - A bibliography. IRE Transactions on Automatic Control 5, 1 (1960), 66 – 70.
53. Cohen, G. H. and Coon, G. A. Theoretical consideration of retarded control. Transactions of the American Society of Mechanical Engineers 76 (1953), 827 – 834.
54. Dahleh, M., Tesi, A. and Vicino, A. On the robust Popov criterion for interval Lur’e system. IEEE Transactions on Automatic Control 38, 9 (September 1993), 1400 – 1405.
55. Dahleh, M. A. and Diaz - Bobillo, I. J. Control of Uncertain Systems: A Linear Programming Approach. Prentice Hall PTR, Englewood Cliffs, NJ, 1995.
56. 1 optimal feedback controllers for discrete - time systems. In Proceedings of the American Control Conference (Seattle, WA, 1986).
57. 1 optimal feedback controllers for MIMO discrete - time systems. IEEE Transactions on Automatic Control AC - 32, 4 (April 1987), 314 – 322.
58. 1 optimal compensators for continuous - time systems. IEEE Transactions on Automatic Control AC - 32 (1987), 889 – 895.
59. Dasgupta, S. A Kharitonov like theorem for systems under nonlinear passive feedback. In Proceedings of the 26th IEEE Conference on Decision and Control (Los Angeles, CA, December 1987), pp. 2062 – 2063.
60. Dasgupta, S. Kharitonov’s theorem revisited. Systems & Control Letters 11 (1988), 381 – 384.
61. Dasgupta, S. and Bhagwat, A. S. Conditions for designing strictly positive real transfer functions for adaptive output error identification. IEEE Transactions on Circuits and Systems CAS - 34 (1987), 731 – 736.
62. Datta, A., Ho, M. T. and Bhattacharyya, S. P. Structure and Synthesis of PID Controllers. Springer - Verlag, London, UK, 2000.
63. Davison, E. J. The output control of linear time - invariant multivariable systems with unmeasurable arbitrary disturbances. IEEE Transactions on Automatic Control AC - 17, 5 (1972), 621 – 630.
64. Davison, E. J. The robust control of a servomechanism problem for linear time - invariant systems. IEEE Transactions on Automatic Control AC - 21, 1 (1976), 25 – 34.
65. deGaston, R. R. E. and Safonov, M. G. Exact calculation of the multiloop stability margin. IEEE Transactions on Automatic Control AC - 33, 2 (February 1988), 156 – 171.
66. Desoer, C. A. and Vidyasagar, M. Feedback Systems: Input - Output Properties. Academic Press, New York, NY, 1975.
67. Desoer, C. A. and Wang, Y. T. Linear time - invariant robust servomechanism problem: A self - contained exposition. Control and Dynamic Systems 16 (1980), 81 – 129.
68. Dieudonné, J. Eléments d’analyse, Tome 1: Fondements de l’analyse moderne. Gauthier - Villars, Editeur, Paris, 1969.
69. Dorato, P., Abdallah, C. and Cerone, V. Linear Quadratic Control: An Introduction. Macmillan Publishing Co., New York, NY, 1994.
70. Dorato, P., Fortuna, L. and Muscato, G. Robust Control for Unstructured Perturbations: An Introduction. Springer - Verlag, 1992. Lecture Notes in Control and Information Sciences.
71. Doyle, J. C. Lecture notes in advances in multivariable control. Tech. rep., ONR/Honeywell Workshop, 1984. Minneapolis, MN.
72. Doyle, J. C., Francis, B. A. and Tannenbaum, A. R. Feedback Control Theory. Macmillan Publishing Company, New York, NY, 1992.
73. ∞ control problems. IEEE Transactions on Automatic Control AC - 34, 8 (August 1989), 831 – 847.
74. Elizondo-Gonzales, C. Necessary and sufficient conditions for robust positivity of polynomic functions via sign decomposition. In Proceedings of the 3rd IFAC Symposium on Robust Control Design (RO - COND) (Prague, Czech Republic, 2000).
75. Faedo, S. A new stability problem for polynomials with real coefficients. Ann. Scuola Norm. Sup. Pisa Sci. Fis. Mat. Ser. 3 - 7 (1953), 53 – 63.
76. Ferreira, P. M. G. The servomechanism problem and the method of the state space in the frequency domain. International Journal of Control 23, 2 (1976), 245 – 255.
77. Ferreira, P. M. G. and Bhattacharyya, S. P. On blocking zeros. IEEE Transactions on Automatic Control AC - 22, 2 (1977), 258 – 259.
78. Foo, Y. K. and Soh, Y. C. Stability analysis of a family of matrices. IEEE Transactions on Automatic Control 35, 11 (November 1990), 1257 – 1259.
79. Francis, B. A., Sebakhy, O. A. and Wonham, W. M. Synthesis of multivariable regulators: The internal model principle. Applide Mathematics and Optimization 1 (1974), 64 – 86.
80. Fu, M. Computing the frequency response of linear systems with parametric perturbation. Systems & Control Letters 15 (1990), 45 – 52.
81. Fu, M. and Barmish, B. R. Polytopes and polynomials with zeros in a prescribed set. IEEE Transactions on Automatic Control AC - 34 (1989), 544 – 546.
82. Fu, M., Olbrot, A. W. and Polis, M. P. Robust stability for time - delay systems: The Edge theorem and graphical tests. IEEE Transactions on Automatic Control 34, 8 (August 1989), 813 – 820.
83. Fujita, M., Namerikawa, T., Matsumura, F. and Uchida, K. µ - synthesis of an electromagnetic suspension system. IEEE Transactions on Automatic Control 40, 3 (1995), 530 – 536.
84. Gantmacher, F. R. The Theory of Matrices, Vol. 2. Chelsea Publishing Company, New York, N.Y., 1959.
85. ∞ error bounds. International Journal of Control 39 (1984), 1115–1193.
86. Glover, K., Limebeer, D. J. N., Doyle, J. C., Kasenally, E. M. and Safonov, M. G. A characterization of all solutions to the four block general distance problem. SIAM Journal on Control and Optimization 29 (1991), 283–324.
87. Green, M. and Limebeer, D. Linear Robust Control. Prentice Hall PTR, Englewood Cliffs, NJ, 1995.
88. Grimble, M. J. and Johnson, M. A. Algorithm for PID controller tuning using lqg cost minimization. In Proceedings of 1997 American Control Conference (Albuquerque, NM, June 1997).
89. Grujic, L. T. and Petkovski, D. On robustness of Lur’e systems with multiple nonlinearities. Automatica 23 (1987), 327 – 334.
90. Gu, K., Kharitonov, V. L. and Chen, J. Stability of Time - Delay Systems. Birkhäuser, Boston, MA, 2003.
91. Guillemin, E. A. The Mathematics of Circuit Analysis. Wiley Publishing Co., New York, 1949.
92. Hinrichsen, D. and Pritchard, A. J. New robustness results for linear systems under real perturbations. In Proceedings of the 27th IEEE Conference on Decision and Control (1988).
93. Hinrichsen, D. and Pritchard, A. J. An application of state space methods to obtain explicit formulae for robustness measures of polynomials. In Robustness in Identification and Control, M. Milanese, R. Tempo, and A. Vicino, Eds. Plenum, New York, 1989, pp. 183 – 206.
94. Hinrichsen, D. and Pritchard, A. J. A robustness measure for linear systems under structured real parameter perturbations. Tech. rep., Institut fur Dynamische Systeme, Bremen, Germany, 1991. Report No. 184.
95. ∞ PID controllers. In Proceedings of the 40th IEEE Conference on Decision and Control (Orlando, FL, December 2001), pp. 255 – 260.
96. Ho, M. T., Datta, A. and Bhattacharyya, S. P. Control system design using low order controllers: Constant gain, PI, and PID. In Proceedings of the 1997 American Control Conference (1997), pp. 571 – 578.
97. Ho, M. T., Datta, A. and Bhattacharyya, S. P. A linear programming characterization of all stabilizing PID controllers. In Proceedings of the 1997 American Control Conference (1997), pp. 3922 – 3928.
98. Ho, M. T., Datta, A. and Bhattacharyya, S. P. Generalizations of the Hermite - Biehler theorem. Linear Algebra and Its Applications 302 - 303 (1999), 135 – 153.
99. Ho, M. T., Datta, A. and Bhattacharyya, S. P. Robust and non - fragile PID controller design. International Journal of Robust and Nonlinear Control 11 (2001), 681 – 708.
100. Ho, M. T. and Lin, C. Y. PID controller design for robust performance. In Proceedings of the 41st IEEE Conference on Decision and Control (Seville, Spain, December 2002), pp. 1063 – 1067.
101. Ho, M. T., Silva, G. J., Datta, A. and Bhattacharyya, S. P. Real and complex stabilization: Stability and performance. In Proceedings of the 2004 American Control Conference (Boston, MA, June 2004), pp. 4126 – 4138.
102. Ho, W., Hang, C. and Zhou, J. Self - tuning PID control for a plant with underdamped response with specification on gain and phase margins. IEEE Transactions on Control Systems Technology 5, 4 (1997), 446 – 452.
103. Hollot, C. V. and Tempo, R. On the Nyquist envelope of an interval plant family. IEEE Transactions on Automatic Control 39, 2 (February 1994), 391 – 396.
104. Hollot, C. V. and Xu, Z. L. When is the image of a multilinear function a polytope? A conjecture. In Proceedings of the 28th IEEE Conference on Decision and Control (Tampa, FL, 1989), pp. 1890 – 1891.
105. Hollot, C. V. and Yang, F. Robust stabilization of interval plants using lead or lag compensators. Systems & Control Letters 14 (1990), 9 – 12.
106. Howze, J. W. and Bhattacharyya, S. P. Robust tracking, error feedback and two degrees of freedom controllers. IEEE Transactions on Automatic Control 42, 7 (1997), 980 – 984.
107. Jury, E. I. Sampled - Data Control Systems. Wiley Publishing Co., New York, 1958.
108. Kalman, R. E. Contribution to the theory of optimal control. Bol. Soc. Matem. Mexico (1960), 102 – 119.
109. Kalman, R. E. When is a linear control system optimal? ASME Transactions Series D (Journal of Basic Engineering) (1964), 51 – 60.
110. Kamen, E. W. and Heck, B. S. Fundamentals of Signals and Systems. Prentice Hall, Upper Saddle River, NJ, 1997.
111. Kang, H. I. Extreme point results for robustness of control systems. PhD thesis, Department of Electrical and Computer Engineering, University of Wisconsin, Madison, Wisconsin, U.S.A., 1992.
112. Karmarkar, J. S. and Siljak, D. D. Stability analysis of systems with time delay. Proceedings of IEEE 117, 7 (1970), 1421 – 1424.
113. Katbab, A. and Jury, E. I. Robust Schur - stability of control systems with interval plants. International Journal of Control 51, 6 (1990), 1343 – 1352.
114. Keel, L. and Bhattacharyya, S. Data based interval controller design. In Proceedings of the 2007 IEEE Conference on Decision and Control (New Orleans, LA, 2007).
115. Keel, L. and Bhattacharyya, S. Controller synthesis free of analytical models: Three term controllers. IEEE Transactions on Automatic Control 53, 9 (2008). To appear.
116. Keel, L. and Bhattacharyya, S. Fixed order multivariable controller synthesis: A new algorithm. In Proceedings of the 2008 IEEE Conference on Decision and Control (Cancun, Mexico, 2008).
117. Keel, L. H. and Bhattacharyya, S. Robust stability of interval matrices: A computational approach. International Journal of Control 62, 6 (1995), 1491 – 1506.
118. Keel, L. H. and Bhattacharyya, S. P. Frequency domain design of interval controllers. In Control of Uncertain Dynamic Systems, S. P. Bhattacharyya and L. H. Keel, Eds. CRC Press, Littleton, MA, September 1991.
119. Keel, L. H. and Bhattacharyya, S. P. Parametric stability margin for multilinear interval control systems. In Proceedings of the 1993 American Control Conference (San Francisco, CA, June 1993).
120. Keel, L. H. and Bhattacharyya, S. P. Stability margin for multilinear interval systems via phase conditions: A unified approach. In Proceedings of the 1993 American Control Conference (San Francisco, CA, June 1993).
121. Keel, L. H. and Bhattacharyya, S. P. Control system design for parametric uncertainty. International Journal of Robust and Nonlinear Control 4, 1 (1994), 87 – 100.
122. Keel, L. H. and Bhattacharyya, S. P. Phase properties of Hurwitz polynominals and segments. Tech. rep., Tennessee State University, November 1994. ISE Report No. ACS - 94 - 2.
123. Keel, L. H. and Bhattacharyya, S. P. Robust parametric classical control design. IEEE Transactions on Automatic Control 39, 7 (1994), 1524 – 1530.
124. Keel, L. H. and Bhattacharyya, S. P. Robust, optimal, or fragile? IEEE Transactions on Automatic Control 42, 8 (1997), 1098 – 1105.
125. Keel, L. H. and Bhattacharyya, S. P. A generalization of Mikhailov’s criterion with applications. In Proceedings of the 2000 American Control Conference (Chicago, IL, June 2000).
126. Keel, L. H. and Bhattacharyya, S. P. Root counting, phase unwrapping, stability and stabilization of discrete time systems. Linear Algebra and Its Application 351 - 352 (2002), 501 – 518.
127. Keel, L. H. and Bhattacharyya, S. P. Direct synthesis of first order controllers from frequency response measurements. In Proceedings of the American Control Control (Portland, OR, June 8 - 10 2005).
128. Keel, L. H. and Bhattacharyya, S. P. PID controller synthesis free of analytical models. In Proceedings of the 16th IFAC World Congress (Prague, Czech Republic, July 4 - 8 2005).
129. Keel, L. H. and Bhattacharyya, S. P. Data driven synthesis of three term digital controllers. In Proceedings of the American Control Conference (Minneapolis, MN, June 14 - 16 2006).
130. Keel, L. H., Bhattacharyya, S. P. and Howze, J. W. Robust control with structured perturbations. IEEE Transactions on Automatic Control AC - 33, 1 (January 1988), 68 – 78.
131. Keel, L. H., Lim, K. B. and Juang, J. N. Robust eigenvalue assignment with maximum tolerance to system uncertainties. AIAA Journal of Guidance, Control, and Dynamics 14, 3 (May - June 1991), 615 – 620.
132. Keel, L. H., Mitra, S. and Bhattacharyya, S. P. Data driven synthesis of three term digital controllers. SICE Journal of Control, Measurement, and System Integration 1, 2 (2008), 102 – 110.
133. Keel, L. H., Rego, J. I. and Bhattacharyya, S. P. A new approach to digital PID controller design. IEEE Transactions on Automatic Control 48, 4 (2003), 687 – 692.
134. Keel, L. H., Shaw, J. and Bhattacharyya, S. P. Robust control of interval systems. In Robust Control. Springer - Verlag, Tokyo, Japan, June 1993.
135. Khalil, H. K. Nonlinear Systems. MacMillan, New York, 1992.
136. Kharitonov, V. L. Asymptotic stability of an equilibrium position of a family of systems of linear differential equations. Differential Uravnen 14 (1978), 2086 – 2088. Translation in Differential Equations, vol. 14, pp. 1483 - 1485, 1979.
137. Kharitonov, V. L. The Routh - Hurwitz problem for families of polynomials and quasipolynomials. Izvetiy Akademii Nauk Kazakhskoi SSR, Seria fizikomatematicheskaia 26 (1979), 69 – 79.
138. Kharitonov, V. L. Interval stability of quasipolynomials. In Control of Uncertain Dynamic Systems, S. P. Bhattacharyya and L. H. Keel, Eds. CRC Press, Littleton, MA, September 1991.
139. Kharitonov, V. L. and Zhabko, A. P. Robust stability of time - delay systems. IEEE Transactions on Automatic Control 39 (1994), 2388 – 2397.
140. Kim, Y. C., Keel, L. H. and Bhattacharyya, S. P. Computer aided control system design: Multiple design objectives. In Proceedings of the European Control Conference (Kos, Greece, July 2 - 5 2007).
141. Kogan, J. Robust Stability and Convexity. Springer - Verlag, New York, NY, 1994.
142. Leal, M. A. and Gibson, J. S. A first - order Lyapunov robustness method for linear systems with uncertain parameters. IEEE Transactions on Automatic Control 35, 9 (September 1990), 1068 – 1070.
143. Luenberger, D. G. Optimization by Vector Space Methods. John Wiley and Sons, New York, 1969.
144. Lur’e, A. I. On Some Nonlinear Problems in the Theory of Automatic Control. H. M. Stationary Office, London, 1957. Russian Edition, 1951.
145. Malik, W., Swaroop, D. and Bhattacharyya, S. P. A linear programming approach to the synthesis of fixed order controllers. IEEE Transactions on Automatic Control 53 (2008). To appear.
146. Mansour, M. Robust stability of interval matrices. In Proceedings of the 28th IEEE Conference on Decision and Control (Tampa, FL, December 1989).
147. Mansour, M. Robust stability in systems described by rational functions. In Control and Dynamic Systems, C. T. Leondes, Ed., vol. 51. Academic Press, New York, NY, 1992, pp. 79 – 128.
148. Mansour, M. and Anderson, B. D. O. Kharitonov’s theorem and the second method of Lyapunov. In Robustness of Dynamic Systems with Parameter Uncertainties, M. Mansour, S. Balemi, and W. Truöl, Eds. Birkhäuser, Berlin, 1992, pp. 3 – 12.
149. Mansour, M. and Kraus, F. J. Argument conditions for Hurwitz and Schur stable polynomials and the robust stability problem. Tech. rep., ETH, Zurich, Tech. Report, 1990.
150. Marden, M. Geometry of Polynomial. American Mathematical Society, Providence, RI, 1966.
151. Marquez, H. J. and Diduch, C. P. On strict positive realness of interval plants. IEEE Transactions on Circuits and Systems 40, 8 (1993), 551 – 552.
152. Marshall, J. E. Control of Time Delay Systems. Peter Peregrinus, London, UK, 1979.
153. Marshall, J. E., Gorecki, H., Korytowski, A. and Walton, K. Time - Delay Systems: Stability and Performance Criteria with Applications. Ellis Horwood, New York, 1992.
154. Martin, J. M. State - space measures for stability robustness. IEEE Transactions on Automatic Control AC - 32, 6 (June 1987), 509 – 512.
155. Meressi, T., Chen, D. and Paden, B. Application of Kharitonov’s theorem to mechanical systems. IEEE Transactions on Automatic Control 38, 3 (March 1993), 488 – 491.
156. Minnichelli, R. J., Anagnost, J. J. and Desoer, C. A. An elementary proof of Kharitonov’s stability theorem with extensions. IEEE Transactions on Automatic Control AC - 34, 9 (1989), 995 – 998.
157. Morari, M. and Zafiriou, E. Robust Process Control. Prentice Hall PTR, Englewood Cliffs, NJ, 1989.
158. Mori, T. and Barnett, S. On stability tests for some classes of dynamical systems with perturbed coefficients. IMA Journal of Mathematical Control and Information 5 (1988), 117 – 123.
159. Mori, T. and Kokame, H. Stability of interval polynomials with vanishing extreme coefficients. In Recent Advances in Mathematical Theory of Systems, Control, Networks, and Signal Processing I. Mita Press, Tokyo, Japan, 1992, pp. 409 – 414.
160. Nett., C., Jacobson, C. and Balas, M. A connection between state - space and doubly coprime fractional representations. IEEE Transactions on Automatic Control AC - 29 (1984), 831 – 832.
161. Newton, G., Gould, L. A. and Kaiser, J. F. Analytical Design of Linear Feedback Controls. John Wiley, New York, NY, 1957.
162. Ohm, D., Howze, J. W. and Bhattacharyya, S. P. Structural synthesis of multivariable controllers. Automatica 21, 1 (January 1985), 35 – 55.
163. Ozguler, A. B. and Kocan, A. A. An analytic determination of stabilizing feedback gains. Tech. rep., Report 321, Institut für Dynamische Systeme, Universitat Bremen, September 1994.
164. Panagopoulos, H., Åström, K. J. and Hägglund, T. Design of PID controllers based on constrained optimization. In Proceedings of 1999 American Control Conference (San Diego, CA, June 1999).
165. Patel, R. V. and Toda, M. Quantitative measures of robustness for multivariable systems. In Proceedings of American Control Conference (San Francisco, CA, May 1980).
166. Pearson, J. B. Compensator design for dynamic optimization. International Journal of Control 9 (1968), 473.
167. Pessen, D. W. A new look at PID controller tuning. ASME Journal of Dynamic Systems, Measurement and Control 116 (1994), 553 – 557.
168. Petersen, I. R. A new extension to Kharitonov’s theorem. In Proceedings of IEEE Conference on Decision and Control (Los Angeles, CA, December 1987).
169. Polyak, B. T. Robustness analysis for multilinear perturbations. In Robustness of Dynamic Systems with Parameter Uncertainties, M. Man - sour, S. Balemi, and W. Truöl, Eds. Birkhäuser, Berlin, 1992, pp. 93 – 104.
170. Pontryagin, L. S. On the zeros of some elementary transcendental function. American Mathematical Society Translation 2 (1955), 95 – 110.
171. Rantzer, A. Kharitonov’s weak theorem holds if and only if the stability region and its reciprocal are convex. International Journal of Nonlinear and Robust Control (1992).
172. Rantzer, A. Stability conditions for polytopes of polynomials. IEEE Transactions on Automatic Control AC - 37 (January 1992), 79 – 89.
173. Rosenbrock, H. H. Computer - Aided Control System Design. Academic Press, New York, N.Y., 1974.
174. Safonov, M. G., Jonckheere, E. A., Verma, M. and Limebeer, D. J. N. Synthesis of positive real multivariable feedback systems. International Journal of Control 45 (1987), 817 – 842.
175. ∞ optimization and Hankel approximation. IEEE Transactions on Automatic Control AC - 30, 3 (March 1985), 279 – 280.
176. Sezer, M. E. and ˘Siljak, D. D. A note on robust stability bounds. IEEE Transactions on Automatic Control 34, 11 (November 1989), 1212 – 1215.
177. Sideris, A. and Sánches Peña, R. S. Fast computation of the multivariable stability margin for real interrelated uncertain parameters. IEEE Transactions on Automatic Control 34, 12 (December 1989), 1272 – 1276.
178. Silva, G. J., Datta, A. and Bhattacharyya, S. P. Controller design via Padé approximation can lead to instability. In Proceedings of the 40th IEEE Conference on Decision and Control (Orlando, FL, 2001).
179. Silva, G. J., Datta, A. and Bhattacharyya, S. P. PI stabilization of first - order systems with time - delay. Automatica 37 (2001), 2025 – 2031.
180. Soh, C. B., Berger, C. S. and Dabke, K. P. On the stability properties of polynomials with perturbed coefficients. IEEE Transactions on Automatic Control AC - 30, 10 (October 1985), 1033 – 1036.
181. Tantaris, R. N., Keel, L. H. and Bhattacharyya, S. P. Stabilization of discrete time systems by first order controllers. IEEE Transactions on Automatic Control 48, 5 (2003), 858 – 861.
182. ∞ design with first order controllers. IEEE Transactions on Automatic Control 51, 8 (2006), 1343 – 1347.
183. Tantaris, R. N., Keel, L. H. and Bhattacharyya, S. P. Stabilization of continuous - time systems by first order controllers. In Proceedings of the 10th IEEE Mediterranean Conference on Control and Automation (Lisbon, Portugal, July 9 - 12, 2002).
184. Tantaris, R. N., Keel, L. H. and Bhattacharyya, S. P. Gain/phase margin design with first order controllers. In Proceedings of the 2003 American Control Conference (Denver, CO, June 4 - 6, 2003).
185. Tesi, A. and Vicino, A. A new fast algorithm for robust stability analysis of linear control systems with linearly correlated parametric uncertainty. Systems & Control Letters 13 (1989), 321 – 329.
186. Tesi, A. and Vicino, A. Robust stability of state - space models with structured uncertainties. IEEE Transactions on Automatic Control 35, 2 (February 1990), 191 – 195.
187. Tesi, A. and Vicino, A. Robustness analysis for linear dynamical systems with linearly correlated parameter uncertainties. IEEE Transactions on Automatic Control 35, 2 (February 1990), 186 – 190.
188. Tesi, A. and Vicino, A. Kharitonov segments suffice for frequency response analysis of plant - controller families. In Control of Uncertain Dynamic Systems, S. P. Bhattacharyya and L. H. Keel, Eds. CRC Press, Littleton, MA, September 1991.
189. Tesi, A. and Vicino, A. Robust absolute stability of Lur’e control systems in parameter space. Automatica 27 (1991), 147 – 151.
190. Tesi, A. and Vicino, A. Robust strict positive realness: New results for interval plant plus controller families. In Proceedings of the 30th IEEE Conference on Decision and Control (Brighton, UK, December 1991), pp. 421 – 426.
191. Thompson, W. M., Vacroux, A. G. and Hoffman, C. H. Application of Pontryagin’s time lag stability criterion to force - reflecting servomechanisms. In Proceedings of the 9th Joint Automatic Control Conference (1968).
192. Tsypkin, Y. Z. and Polyak, B. T. Robust absolute stability of continuous systems. In Robustness of Dynamic Systems with Parameter Uncertainties, M. Mansour, S. Balemi, and W. Truöl, Eds. Birkhäuser, Berlin, 1992, pp. 113 – 124.
193. Siljak, D. D. Polytopes of nonnegative polynomials. In Proceedings of the 1989 American Control Conference (Pittsburgh, PA, June 1989).
194. Vaidyanathan, P. and Mitra, S. K. A unified structural interpretation of some well - known stability test procedures for linear systems. IEEE Proceedings 75 (April 1987), 478 – 497.
195. Vicino, A. and Tesi, A. Regularity condition for the stability margin problem with linear dependent perturbations. SIAM Journal on Control and Optimization 33, 5 (May 1995).
196. Vicino, A., Tesi, A. and Milanese, M. Computation of nonconser - vative stability perturbation bounds for systems with nonlinearly correlated uncertainties. IEEE Transactions on Automatic Control AC - 35, 7 (July 1990), 835 – 841.
197. Vidyasagar, M. Control System Synthesis: A Factorization Approach. MIT Press, Cambridge, MA, 1985.
198. Vidyasagar, M. Optimal rejection of persistent bounded disturbances. IEEE Transactions on Automatic Control AC - 31, 6 (June 1986).
199. Voda, A. A. and Landau, I. D. A method of the auto - calibration of PID controllers. Automatica 31, 1 (1995), 41 – 53.
200. Wonham, W. M. Linear Multivariable Control: A Geometric Approach, 3rd Edition. Springer - Verlag, New York, 1985. 2nd Edition.
201. Wonham, W. M. and Pearson, J. B. Regulation and internal stabilization in linear multivariable systems. SIAM Journal in Control 12 (1974), 5 – 8.
202. Xu, H., Datta, A. and Bhattacharyya, S. P. Computation of all stabilizing PID gains for digital control systems. IEEE Transactions on Automatic Control 46, 4 (2001), 647 – 652.
203. Xu, H., Datta, A. and Bhattacharyya, S. P. PID stabilization of lti plants with time - delay. In Proceedings of the 42nd IEEE Conference on Decision and Control (Maui, HI, December 9 - 12, 2003), pp. 4038 – 4043.
204. Yamamoto, S. and Hashimoto, I. Present status and future needs: The view from Japanese industry. In Proceedings of the 4th International Conference on Chemical Process Control (Tokyo, Japan, December 1991), Springer - Verlag.
205. Yedavalli, R. K. Improved measures of stability for linear state space model. IEEE Transactions on Automatic Control AC - 30, 6 (June 1985), 577 – 579.
206. Yedavalli, R. K. and Liang, Z. Reduced conservatism in stability robustness bounds by state transformation. IEEE Transactions on Automatic Control AC - 31, 9 (September 1986), 863 – 865.
207. Yeung, K. S. and Wang, S. S. A simple proof of Kharitonov’s theorem. IEEE Transactions on Automatic Control 32 (April 1987), 822 – 823.
208. Zadeh, L. A. and Desoer, C. A. Linear Systems Theory. McGraw Hill, New York, 1963.
209. Zames, G. Functional analysis applied to nonlinear feedback systems. IEEE Transactions on Circuit Theory (September 1963), 392 – 404.
210. Zames, G. On the input - output stability of time - varying nonlinear feedback systems - Parts I and II. IEEE Transactions on Automatic Control AC - 11 (1966), 228 – 238 and 465 – 476.
211. Zames, G. Feedback and optimal sensitivity: Model reference transformations, multiplicative seminorms, and approximate inverses. IEEE Transactions on Automatic Control AC - 26 (April 1981), 301 – 320.
212. Zames, G. and Francis, B. A. Feedback, minimax sensitivity, and optimal robustness. IEEE Transactions on Automatic Control AC - 28 (May 1983), 585 – 601.
213. Zhou, K., Doyle, J. C. and Glover, K. Robust Optimal Control. Prentice Hall PTR, Englewood Cliffs, NJ, 1995.
214. Zhou, K. and Khargonekar, P. P. Stability robustness bounds for linear state space models with structured uncertainty. IEEE Transactions on Automatic Control AC - 32 (1987), 621 – 623.
215. Zhuang, M. and Atherton, D. P. Automatic tuning of optimum PID controllers. IEE Proceedings - D 140, 3 (1993), 216 – 224.
216. Ziegler, J. G. and Nichols, N. B. Optimum settings for automatic controllers. Transactions of the American Society of Mechanical Engineers 64 (1942), 759 – 768.