Minimax guaranteed cost control of uncertain non-linear systems

International Journal of Control

Volumn 73, Issue 16, 2000, Pages 1491-1499

  Aliyu, M D S ^a  

^a LOUISIANA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CLOSED LOOP CONTROL SYSTEMS; CONTROL EQUIPMENT; COSTS; FEEDBACK CONTROL; NONLINEAR SYSTEMS; ROBUSTNESS (CONTROL SYSTEMS); VECTORS;

DISSIPATIVE FEEDBACK;

UNCERTAIN SYSTEMS;

EID: 0034634822     PISSN: 00207179     EISSN: 13665820     Source Type: Journal    
DOI: 10.1080/00207170050163350     Document Type: Article

References (31)

1. Aliyu, M. D. S., 1999a, Robust stabilization of nonlinear uncertain systems under matching conditions, Proceedings of the 37th IEEE Conference on Decision and Control, Tampa, Florida, December, pp. 4087-4091.
2. Aliyu, M. D. S., 1999 b, Guaranteed cost control of uncertain nonlinear systems: a minimax approach. IEEE Proceeding Conference on Decision and Control, Phoenix, Arizona, USA, December, pp. 2485-2490.
3. ∞-control. Submitted to IEEE Transactions on Automatic Control.
4. Byrnes, C. I., Isidori, A., and Willems, J. C., 1991, Passivity, feedback equivalence and global stabilization of minimum-phase nonlinear systems. IEEE Transactions on Automatic Control, 36, 1228-1240.
5. Chang, S. S. L., and Peng, T. K. C., 1972, Adaptive guaranteed cost control of systems with uncertain parameters. IEEE Transactions on Automatic Control, 17, 474-483.
6. Geromel, J. C., and Yamakami A., 1985, On the robustness of nonlinear regulators and its application to nonlinear systems stabilization, IEEE Transactions on Automatic Control, 30, 1251-1254.
7. Glad, S. T., 1984, On the gain margin of nonlinear and optimal regulators. IEEE Transactions on Automatic Control, 29, 615-620.
8. Glad, S. T., 1987, Robustness of nonlinear state feedback—A survey. Automatica, 23, 425-435.
9. Gutman, S., 1979, Uncertain dynamical Systems—A Lyapunov min-max approach. IEEE Transactions on Automatic Control, 24, 437-443.
10. Hill, D., and Moylan, P., 1976, The stability of nonlinear dissipative systems. IEEE Transactions on Automatic Control, 21, 708-711.
11. Isidori, A., 1992, Feedback control of nonlinear systems. International Journal of Robust and Nonlinear Control, 2, 291-311.
12. Isidori, A., 1994, control via measurement feedback for nonlinear systems. International Journal of Robust and Nonlinear Control, 4, 553-574.
13. Khargonekar, P. P., Petersen, I. R., and Zhou K., 1990, Robust stabilization of uncertain linear systems: quadratic stabilizability and control theory. IEEE Transactions on Automatic Control, 35, 356-361.
14. Moheimani, S. O. R., and Petersen, I. R., 1998, Guaranteed cost control of uncertain systems with a time-multiplied quadratic cost function: an approach based on linear matrix inequalities. Automatica, 34, 651-654.
15. Nguang, S. K., 1996, Robust nonlinear output feedback control. IEEE Transactions on Automatic Control, 41, 1003-1007.
16. 2-approach. International Journal of Robust and Nonlinear Control, 6, 691-726.
17. Petersen, I. R., 1987, A stabilization algorithm for a class of uncertain linear systems. Systems and Control Letters, 8, 351-357.
18. Petersen, I. R., and MacFarlane, D., 1992, Optimal guaranteed cost control of uncertain linear systems. Proceeding. American Control Conference, Chicago, Illinois, USA, June, pp. 2929-2930.
19. Petersen, I. R., and MacFarlane, D., 1994, Optimal guaranteed cost control and filtering for uncertain linear systems. IEEE Transactions on Automatic Control, 39, 1971-1977.
20. Savkin, A. V., and Petersen, I. R., 1995 a, Structured dissipativeness and absolute stability of nonlinear systems. International Journal of Control, 62, 443-460.
21. Savkin, A. V., and Petersen, I. R., 1995 b, An uncertainty averaging approach to optimal guaranteed cost control of uncertain systems with structured uncertainty. Automatica, 31, 1649-1653.
22. Savkin, A. V., and Petersen, I. R., 1997a, Output feedback guaranteed cost control of uncertain systems on an infinite time interval. International Journal of Robust and Nonlinear Control, 7, 43-58.
23. Savkin, A. V., and Petersen, I. R., 1997b, Optimal guaranteed cost control of discrete-time uncertain nonlinear systems. IMA Journal of Mathematical Control and Information, 14, 319-332.
24. ∞control of uncertain nonlinear systems via state feedback. IEEE Transactions on Automatic Control, 40, 766-769.
25. ∞nonlinear control via measurement feedback. International Journal of Robust and Nonlinear Control, 7, 975-987.
26. ∞control. IEEE Transactions on Automatic Control, 37, 770-784.
27. 2-gain bounded uncertainty. Sytems and Control Letters, 24, 75-81.
28. VIDYASAGAR, M., 1995, Nonlinear Systems Analysis (New Jersey: Prentice Hall International).
29. Willems, J. C., 1972, Dissipative dynamical systems: Part I General theory, Part II: Linear systems with quadratic supply rates. Archives for Rational Mechanics and Analysis, 45, 321-393.
30. ∞control for linear systems with norm-bounded time-varying uncertainty. IEEE Transactions on Automatic Control, 37, 1188-1191.
31. Zames, G., 1981, Feedback and optimal sensitivity: model reference transformations, multiplicative semi-norms and approximate inverses. IEEE Transactions on Automatic Control, 26, 301-320.