Stability of linear time-varying delay systems and applications to control problems

Journal of Computational and Applied Mathematics

Volumn 194, Issue 2, 2006, Pages 343-356

  Phat, Vu N ^a   Niamsup, Piyapong ^b  

^a INSTITUTE OF MATHEMATICS   (Viet Nam)

^b CHIANG MAI UNIVERSITY   (Thailand)

Author keywords

Exponential stability; Lyapunov function; Matrix inequalities; Riccati equation; Time delay; Time varying

Indexed keywords

LYAPUNOV METHODS; MATRIX ALGEBRA; NONLINEAR CONTROL SYSTEMS; NUMERICAL METHODS; PROBLEM SOLVING; RICCATI EQUATIONS;

EXPONENTIAL STABILITY; LINEAR MATRIX INEQUALITIES (LMI); TIME DELAYS; TIME-VARYING;

TIME VARYING CONTROL SYSTEMS;

EID: 33646526977     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2005.07.021     Document Type: Article

References (24)

1. Abou-Kandil H., Freiling G., Ionescu V., and Jank G. Matrix Riccati Equations in Control and Systems Theory (2003), Birkhauser, Basel
2. S. Boyd, El. Ghaoui, E. Feron, V. Balakrishnan, Linear matrix inequalities and control theory, SIAM Studies in Applied Mathematics, vol. 15, SIAM, Philadelphia, PA, 1994.
3. Cao D.Q., He P., and Zhang K. Exponential stability criteria of uncertain systems with multiple time delays. J. Math. Anal. Appl. 283 (2003) 362-374
4. Cao J., and Wanfg J. Delay-dependent robust stability of uncertain nonlinear systems with time delays. Appl. Math. Comput. 154 (2004) 289-297
5. Chen M.S., and Chen Y.Z. Static output feedback control for periodically time-varying systems. IEEE Trans. Automat. Control 44 (1999) 218-221
6. Fridman E., and Shaked U. A descriptor system approach to H-infinity control of linear time-delay systems. IEEE Trans. Automat. Control 47 (2002) 253-270
7. Gibson J.S. Riccati equations and numerical approximations. SIAM J. Contr. Optim. 21 (1983) 95-139
8. Hartung F. Linearized stability in periodic functional differential equations with state-dependent delays. J. Comput. Appl. Math. 174 (2005) 201-211
9. Jefferey J.D. Stability for time varying linear dynamic systems on time scales. J. Comput. Appl. Math. 176 (2005) 381-410
10. Kalman R. Contribution to the theory of optimal control. Bol. Soc. Mat. Mexicana 5 (1960) 102-119
11. Kharitonov V.L. Lyapunov-Krasovskii functionals for scalar time delay equations. Systems Control Lett. 51 (2004) 133-149
12. Kharitonov V.L., and Hinrichsen D. Exponential estimates for time delay systems. Systems Control Lett. 53 (2004) 395-405
13. Klamka J. Controllability of Nonlinear Dynamical Systems (1990), Kluwer Academic Publisher, Berlin
14. Kolmanovskii V.B., and Nosov V.R. Stability of Functional Differential Equations (1986), Academic Press, London
15. Laub A.J. Schur techniques for Riccati differential equations. Feedback Control of Linear and Nonlinear Systems, Lecture Notes in Control and Information Sciences (1982), Springer, Berlin 165-174
16. Liu P.L., and Su T.J. Robust stability of interval time-delay systems with delay-dependence. Systems Control Lett. 33 (1998) 231-239
17. Niamsup P., and Phat V.N. Asymptotic stability of nonlinear control systems described by differential equations with multiple delays. Electron. J. Diff. Equations 11 (2000) 1-17
18. Phat V.N. New stabilization criteria for linear time-varying systems with state delay and normed bounded uncertainties. IEEE Trans. Atomat. Control 12 (2002) 2095-2098
19. Phat V.N., and Bay N.S. Stability analysis of nonlinear retarded difference equations in Banach spaces. J. Comput. Math. Appl. 45 (2003) 951-960
20. Sun Y.J., and Hsieh J.G. On α-stability criteria of nonlinear systems with multiple delays. J. Franklin Inst. 335B (1998) 695-705
21. William Thomas R. Riccati Differential Equations (1972), Academic Press, New York
22. Xu B. Stability criteria for linear systems with uncertain delays. J. Math. Anal. Appl. 284 (2003) 455-470
23. Xu S., and Lam J. Improved delay-dependent stability criteria for time-delay systems. IEEE Trans. Automat. Control 50 (2005) 384-387
24. Xu S., Lam J., and Zou Y. A simplified descriptor system approach to delay-dependent stability and performance analyses for time-delay systems. IEE Proc.-Control Theory and Applications 152 (2005) 147-151