H∞ control for nonlinear time-varying delay systems with convex polytopic uncertainties

Nonlinear Analysis, Theory, Methods and Applications

Volumn 72, Issue 11, 2010, Pages 4254-4263

  Niamsup, P ^a   Phat, V N ^b  

^a CHIANG MAI UNIVERSITY   (Thailand)

^b INSTITUTE OF MATHEMATICS   (Viet Nam)

Author keywords

Linear matrix inequalities; Lyapunov function; Nonlinear H control; Polytopic uncertainties; Stability; Time varying delay

Indexed keywords

CONVEX POLYTOPIC UNCERTAINTY; DELAY-DEPENDENT; EXPONENTIAL STABILITY; LYAPUNOV-KRASOVSKII FUNCTIONALS; NONLINEAR H; NUMERICAL EXAMPLE; OPTIMAL CONTROLS; POLYTOPIC UNCERTAINTIES; SUFFICIENT CONDITIONS; TIME VARYING DELAY SYSTEMS; TIME-VARYING DELAY;

CLOSED LOOP SYSTEMS; DIFFERENTIAL EQUATIONS; LYAPUNOV FUNCTIONS; NONLINEAR SYSTEMS; SWITCHING SYSTEMS; SYSTEM STABILITY; THREE TERM CONTROL SYSTEMS; TIME VARYING CONTROL SYSTEMS; UNCERTAIN SYSTEMS;

LINEAR MATRIX INEQUALITIES;

EID: 77949492078     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2010.02.001     Document Type: Article

References (29)

1. Agarwal R.P., Bohner M., and Li W.T. Nonoscillation and Oscillation: Theory of Functional Differential Equations (2004), Marcel Dekker, New York
2. Chukwu E.N. Stability and Time-optimal Control of Hereditary Systems (1992), Academic Press, Inc., Boston, San Diego, New York
3. Lakshmikantham V., and Leela S. A technique in stability theory for delay differential equations. Nonlinear Anal. TMA 3 (1979) 317-323
4. Lakshmikantham V., Leela S., and Martynyuk M. Stability Analysis of Nonlinear Systems (1989), Marcel Dekker, New York
5. ∞ control for uncertain fuzzy systems with time-varying delays. Nonlinear Anal. TMA 68 (2008) 1352-1361
6. Phat V.N., and Niamsup P. Stability analysis for a class of functional differential equations and applications. Nonlinear Anal. TMA 71 (2009) 6265-6275
7. ∞ Control Theory (1987), Springer-Verlag, Berlin
8. ∞ Methods (2000), Springer-Verlag, London
9. P. Colaneri, J.C. Geromel, Parameter dependent Lyapunov function for time-varying polytopic systems, in: Proc. Amer. Contr. Conf., Portland, OR, vol. 6, 2005, pp. 604-608.
10. A.G. Spark, Analysis of affine parameter-varying systems using parameter dependent Lyapunov functions, in: Proc. of 36th IEEE CDC, California, USA, December, 1997, pp. 990-991.
11. ∞ control of linear time-varying systems: A state-space approach. SIAM J. Control Optim. 29 (1991) 1394-1413
12. ∞ control for uncertain systems with time-varying delays. IET Contr. Theory Appl. 145 (1988) 338-344
13. ∞ state-feedback control of continuous-time systems with state delays. IEEE Trans. Automat. Control 45 (2000) 2406-2411
14. ∞ control for heat exchangers controlled by the manipulation of flow rate. Nonlinear Anal. TMA 30 (1997) 2237-2248
15. ∞ control and exponential stability for a class of nonlinear non-autonomous systems with time-varying delay. J. Optim. Theory Appl. 142 (2009) 603-618
16. ∞ control for systems with time varying delays. Automatica 42 (2006) 43-348
17. Phat V.N., and Nam P.T. Exponential stability and stabilization of uncertain linear time-varying systems using parameter dependent Lyapunov function. Int. J. Control 8 (2007) 1333-1341
18. Park J.H., and Kwon O. Novel stability criterion of time delay systems with nonlinear uncertainties. Appl. Math. Lett. 18 (2005) 683-688
19. ∞ filtering for neutral delay differential systems. Appl. Math. Comput. 150 (2004) 235-244
20. ∞ filter for a class of neutral systems: LMI optimization approach. Math. Comput. Simulation 70 (2005) 99-109
21. Park J.H. Novel robust stability criterion for a class of neutral systems with mixed delays and nonlinear perturbations. Appl. Math. Comput. 161 (2005) 413-421
22. Mori T., and Kokame H. A parameter-dependent Lyapunov function for a polytope of matrices. IEEE Trans. Automat. Control 45 (2000) 1516-1519
23. He Y., Wu M., She J.H., and Liu G.P. Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic-type uncertainties. IEEE Trans. Automat. Control 49 (2003) 828-832
24. Gao H., Meng X., and Chen T. A parameter-dependent approach to robust filtering for time-delay systems. IEEE Trans. Automat. Control 53 (2008) 2420-2425
25. ∞ filtering for uncertain time-delay systems: Matrix inequality approach. J. Optim. Theory Appl. 129 (2006) 309-324
26. ∞ filtering for uncertain discrete-time systems. Automatica 45 (2009) 560-565
27. Boyd S., Ghaoui L.E., Feron E., and Balakrishnan V. Linear Matrix Inequalities in System and Control Theory (1994), SIAM, Philadelphia
28. Hale J.K., and Verduyn Lunel SM. Introduction to Functional Differential Equations (1993), Springer-Verlag, New York
29. Mondie S., and Kharitonov V.L. Exponential estimates for retarded time-delay systems: An LMI approach. IEEE Trans. Automat. Control 50 (2005) 268-273