Robust exponential stability and stabilization of linear uncertain polytopic time-delay systems

Journal of Control Theory and Applications

Volumn 6, Issue 2, 2008, Pages 163-170

  Nam, Phan T ^a   Phat, Vu N ^b  

^a Quynhon University   (Viet Nam)

^b INSTITUTE OF MATHEMATICS   (Viet Nam)

Author keywords

Exponential stability; Linear matrix inequalities; Parameter dependent Lyapunov function; Polytopic time delay system; Stabilization

Indexed keywords

AUTOMATION; CONTROL THEORY; DELAY CONTROL SYSTEMS; EIGENVALUES AND EIGENFUNCTIONS; LINEAR CONTROL SYSTEMS; LINEAR MATRIX INEQUALITIES; MATRIX ALGEBRA; MILITARY DATA PROCESSING; SYSTEM STABILITY; TIME DELAY;

CONTROL DESIGN METHODS; EDITORIAL BOARD; EXPONENTIAL STABILITY; LINEAR MATRIX IN EQUALITIES (LMI); LMI APPROACH; LYAPUNOV FUNCTIONALS; NUMERICAL EXAMPLES; ROBUST EXPONENTIAL STABILITY; SOUTH CHINA UNIVERSITY OF TECHNOLOGY; STABILIZATION PROBLEMS; SUFFICIENT CONDITIONS (SC); TIME DELAY SYSTEMS;

STABILIZATION;

EID: 47049093280     PISSN: 16726340     EISSN: 10008152     Source Type: Journal    
DOI: 10.1007/s11768-008-6104-4     Document Type: Article

References (22)

1. E. N. Chukwu. Stability and Time-Optimal Control of Hereditary Systems[M]. Boston, San Diego, New York: Academic Press, Inc., 1992.
2. J. J. DaCunha. Stability for time-varying linear dynamical systems on time scale[J]. Journal of Computer Application Mathematica, 2000, 176(1): 381-410.
3. V. L. Kharitonov, D. Hinrichsen. Exponential estimates for time-delay systems[J]. Systems and Control Letters, 2004, 53(2): 395-405.
4. V. B. Kolmanovskii, S. Niculescu, J. P. Richard. On the Lyapunov-Krasovskii functionals for stability analysis of linear delay systems[J]. International Journal of Control, 1999, 72(2): 374-384.
5. V. N. Phat, S. Pairote. Global stabilization of linear periodically time-varying switched systems via matrix inequalities[J]. Journal of Control Theory and Applications, 2006, 4(1): 24-29.
6. V. N. Phat, A. V. Savkin. Robust state estimation for a class of linear uncertain time-delay systems[J]. Systems & Control Letters, 2002, 47(2): 237-245.
7. V. N. Phat. Weak asymptotic stabilizability of discrete-time inclusions given by set-valued operators[J]. Journal of Mathematical Analysis Application, 1996, 202(2): 353-369.
8. V. N. Phat, P. T. Nam. Exponential stability criteria of linear non-autonomous systems with multiple delays[J]. Electronic Journal of Differencial Equations, 2005, 2005(58): 1-9.
9. T. Yoshizawa. Stability Theory by Lyapunov's Second Method[M]. Tokyo: Publication of the Mathematic Society, 1966.
10. S. Boyd, L. El Ghaou, E. Feron, et al. Linear matrix inequalities in system and control theory[M]//Studies in Applied Mathematics, Philadenphia: SIAM, 1994.
11. P. Colaneri, J. C. Geromel. Parameter dependent Lyapunov function for time-varying polytopic systems[C]// Proceedings of the American Control Conference. Portland OR: IEEE, 2005: 604-608.
12. J. Daafouz, J. Bernusson. Pararmeter dependent Lyapunov functions for discrete-time systems with time varying parametric uncertaintiey[J]. Systems & Control Letters, 2001, 43(2): 355-359.
13. E. Feron, P. Apkarian, P. Gahinet. Analysis and synthesis of robust control systems via parameter dependent Lyapunov functions[J]. IEEE Transactions on Automatic Control, 1996, 41(7): 1041-1046.
14. T. Mori, H. Kokame. A parameter-dependent Lyapunov function for a polytope of matrices[J]. IEEE Transactions on Automatic Control, 2000, 45(8): 1516-1519.
15. A. G. Spark. Analysis of affinely parameter-varying systems using parameter dependent Lyapunov functions[C]//Proceedings Conference on Decision and Control. California, USA: IEEE, 997: 990-991.
16. Y. Jia. Alternative proofs for inproved LMI representations for the analysis and the design of continuous-time systems with polytopic type uncertainty: a predective approach[J]. IEEE Transactions on Automatic Control, 2003, 48(10): 1413-1416.
17. J. Bernusson, P. L. Peres, J. C. Geromel. A linear programming oriented procedure for quadratic stabilization of uncertain systems[J]. Systems & Control Letters, 1989, 13(1): 65-72.
18. D. C. Ramos, P. L. D. Peres. An LMI condition for the robust stability of uncertain continuous time linear systems[J]. IEEE Transactions on Automatic Control, 2002, 47(4): 675-678.
19. K. Tanaka, T. Hori, H. O. Wang. A multiple Lyapunov function approach to stabilization of fuzzy control systems[J]. IEEE Transactions on Automatic Control, 2003, 11(4): 582-589.
20. Y. He, M. Wu, J. She, et al. Parameter-dependent Lyapunov functional for stability fo time-delay systems with polytopic-type uncertainties[J]. IEEE Transactions on Automatic Control, 2004, 49(5): 828-832.
21. Q. Xia, M. Jia. Robust stability functional of state delayed systems with polytopic type uncertainties via parameter dependent Lyapunov functions[J]. International Journal of Control, 2002, 75(16): 1427-1434.
22. S. Mondie, V. L. Kharitonov. Exponential estimates for retarded time-delay systems: an LMI approach[J]. IEEE Transactions on Automatic Control, 2005, 50(2): 268-273.