Robust mixed H2/H∞ state-feedback control for continuous-time descriptor systems with parameter uncertainties

Circuits, Systems, and Signal Processing

Volumn 24, Issue 4, 2005, Pages 431-443

  Xia, Yuanqing ^a,b   Shi, Peng ^a   Liu, Guoping ^a   Rees, David ^a  

^a UNIVERSITY OF GLAMORGAN   (United Kingdom)

^b BEIJING INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Linear matrix inequality; Mixed H2 H control; Robustness; State feedback; Uncertain descriptor systems

Indexed keywords

CONSTRAINT THEORY; CONTROL SYSTEM ANALYSIS; CONTROL SYSTEM SYNTHESIS; FEEDBACK CONTROL; MATRIX ALGEBRA; OPTIMIZATION; PERTURBATION TECHNIQUES; ROBUSTNESS (CONTROL SYSTEMS); STATE FEEDBACK; THEOREM PROVING; UNCERTAIN SYSTEMS;

LINEAR MATRIX INEQUALITY (LMI); TRANSFER MATRIX; UNCERTAIN DESCRIPTOR SYSTEMS;

OPTIMAL CONTROL SYSTEMS;

EID: 26444527425     PISSN: 0278081X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00034-004-0917-2     Document Type: Article

References (38)

1. ∞ performance bound: A Riccati equation approach, IEEE Trans. Automat. Control, 34, 293-305, 1989.
2. S. Boyd, L. El. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, 1994.
3. E. K. Boukas, Stabilization of stochastic nonlinear hybrid systems, Internat. J. Innovative Computing, Information and Control, 1(1), 131-141, 2005.
4. ∞ control for linear Markovian jump systems with unknown nonlinearities, J. Math. Anal. Appl., 282(1), 241-255, 2003.
5. L. Dai, Singular Control System, Springer-Verlag, Berlin, 1989.
6. ∞ control problems, IEEE Trans. Automat. Control, 34, 831-847, 1989.
7. ∞ performance objective, Proceedings of the American Control Conference, Pittsburgh, PA, 2065-2070, 1989.
8. ∞ performance objective II: Optimal control, IEEE Trans. Automat. Control, 39, 1575-1587, 1994.
9. V. Dragan, The linear quadratic optimization problem for a class of singularly perturbed stochastic systems, Internat. J. Innovative Computing, Information and Control, 1(1), 53-63, 2005.
10. ∞ approach, Automatica, 35(8), 1369-1378, 1999.
11. C. A. Fang and F. R. Chang, Analysis of stability robustness for generalized state-space systems with structured perturbations, Systems Control Lett., 21, 109-114, 1993.
12. ∞ control, Internat. J. Robust Nonlinear Control, 4, 421-448, 1994.
13. ∞ control for continuous-time linear systems, Proceedings of 31th Conf. Decision & Control, Arizona, USA, 487-492, 1992.
14. ∞ norm bound and relations to risk sensitivity, Systems Control Lett. 11, 167-172, 1988.
15. 2 control of descriptor systems, Proceedings of 39th Conf. Decision & Control, Australia, 167-172, 2000.
16. T. Iwasaki, Robust performance analysis for systems with structured uncertainty, Internat. J. Robust Nonlinear Control, 6, 85-99, 1996.
17. ∞ control: A convex optimization approach, IEEE Trans. Automat. Control, 36, 824-837, 1991.
18. C. Lin, J. L. Wang, G. Yang, and J. Lam, Robust stabilization via state feedback for descriptor systems with uncertainties in the derivative, Internat. J. Control, 73, 407-415, 1991.
19. M. Mahmoud and P. Shi, Robust stability, stabilization and H-infinity control of time-delay systems with Markovian jump parameters, Internat. J. Robust Nonlinear Control, 13(8), 755-784, 2003.
20. ∞ control for descriptor systems: A matrix inequalities approach, Automatica, 33, 669-673, 1997.
21. 2 performance, IEEE Trans. Automat. Control, 44, 38-49, 1999.
22. L. Qiu and E. J. Davison, The stability robustness of generalized eigenvalues, IEEE Trans. Automat. Control, 37, 886-891, 1999.
23. ∞ control, Automatica, 27, 307-316, 1991.
24. ∞ control, IEEE Trans. Automat. Control, 40, 1054-1062, 1995.
25. P. Shi, E. K. Boukas, and R. K. Agarwal, Control of Markovian jump discrete-time systems with norm bounded uncertainty and unknown delay, IEEE Trans. Automat. Control, 44(11), 2139-2144, 1999.
26. 2 control problem: A worst-case design, IEEE Trans. Automat. Control, 38, 1564-1574, 1993.
27. 2 control of descriptor system with time-varying uncertainty, Internat. J. Control, 71, 559-579, 1998.
28. 2 performance of uncertain descriptor system, Proceedings of the European Control Conference, WE-E-B2, 1997.
29. ∞ control of descriptor systems, Proceedings of 38th Conference Decision & Control, USA, 4092-4097, 1999.
30. G. Verghese, B. C. Levy, and T. Kailath, A generalized state-space for singular systems, IEEE Trans. Automat. Control, 26, 811-831, 1981.
31. ∞ control descriptor systems, Proceedings of American Control Conference, Albuquerque, Texas, Session TM14.3, 1997.
32. Y. Xia and Y. Jia, Robust sliding mode control for uncertain time-delay systems: An LMI approach, IEEE Trans. Automat. Control, 48(6), 1086-1092, 2003.
33. Y. Xia and Y. Jia, Robust control of state delayed systems with polytopic type uncertainties via parameter-dependent Lyapunov functionals, Systems Control Lett., 50(3), 183-193, 2003.
34. ∞ control of systems with parameter uncertainty, Internat. J. Control, 63, 741-750, 1996.
35. S. Xu and C. Yang, An algebraic approach to the robust stability analysis and robust stabilization of uncertain singular systems, Internat. J. Systems Science, 31, 55-61, 2000.
36. ∞ controllers for singular systems, IEEE Trans. Circuits and Systems II, 50, 615-626, 2003.
37. Q. L. Zhang and X. H. Xu, Robust stabilization of descriptor systems, Proceedings of 33rd IEEE Conference on Decision and Control, Lake Buena Vista, FL, 2981-2982, 1994.
38. ∞ performance objective I: Robust performance analysis, IEEE Trans. Automat. Control, 39, 1564-1574, 1994.