Robust stability of nonlinear time-delay systems with interval time-varying delay

International Journal of Robust and Nonlinear Control

Volumn 21, Issue 7, 2011, Pages 709-724

  Orihuela, L ^a   Millan, P ^a   Vivas, C ^a   Rubio, F R ^a  

^a UNIVERSITY OF SEVILLE   (Spain)

Author keywords

linear matrix inequalities; Lyapunov Krasovskii; nonlinear uncertainties; time delay systems; time varying delays

Indexed keywords

DELAY-DEPENDENT; DELAY-DEPENDENT STABILITY CONDITION; GAIN ANALYSIS; INTEGRAL TERMS; INTERVAL TIME-VARYING DELAYS; LMI-CONDITION; LOWER AND UPPER BOUNDS; LYAPUNOV-KRASOVSKII; LYAPUNOV-KRASOVSKII FUNCTIONALS; MULTIPLE REGIONS; NONLINEAR TIME-DELAY SYSTEMS; NONLINEAR UNCERTAINTIES; ROBUST STABILITY; TIME VARYING UNCERTAINTIES; TIME-DELAY SYSTEMS; TIME-VARYING DELAY; TIME-VARYING DELAYS;

DELAY CONTROL SYSTEMS; LYAPUNOV FUNCTIONS; TIME DELAY; TIME VARYING CONTROL SYSTEMS; UNCERTAIN SYSTEMS; UNCERTAINTY ANALYSIS;

LINEAR MATRIX INEQUALITIES;

EID: 79952827224     PISSN: 10498923     EISSN: 10991239     Source Type: Journal    
DOI: 10.1002/rnc.1616     Document Type: Article

References (26)

1. Richard JP,. Time-delay systems: an overview of some recent advances and open problems. Automatica 2003; 39 (10): 1667-1694.
2. Mahmoud MS,. Robust Control and Filtering for Time-delay Systems. Marcel Dekker, Inc.: New York, 2000.
3. Kolmanovskii VB, Richard JP,. Stability of some linear systems with delays. IEEE Transactions on Automatic Control 1999; 44 (5): 984-989.
4. Park P,. A delay-dependent stability criterion for systems with uncertain time-invariant delays. IEEE Transactions on Automatic Control 1999; 44 (4): 876-877.
5. Moon YS, Park P, Kwon WH, Lee YS,. Delay-dependent robust stabilization of uncertain state-delayed systems. International Journal of Control 2001; 74 (14): 1447-1455.
6. Xu S, Lam J,. Improve delay-dependent stability criteria for time-delay systems. IEEE Transactions on Automatic Control 2005; 50 (3): 384-387. (Pubitemid 40448589)
7. Hespanha J, Naghshtabrizi P, Xu Y,. A survey of recent results in networked control systems. Proceedings of the IEEE, Special Edition 2007; 95 (1): 138-162.
8. Fridman E, Shaked U,. An improved stabilization method for linear time-delay systems. IEEE Transactions on Automatic Control 2002; 47 (11): 1931-1937. (Pubitemid 35426901)
9. He Y, Wang QG, Xie L, Lin C,. Further improvement of free-weighting matrices technique for systems with time-varying delay. IEEE Transactions on Automatic Control 2007; 52 (2): 293-299. (Pubitemid 46444284)
10. Jiang X, Han QL,. Delay-dependent robust stability for uncertain linear systems with interval time-varying delay. Automatica 2006; 42 (6): 1059-1065.
11. Shao H,. New delay-dependent stability criteria for systems with interval delay. Automatica 2009; 45 (3): 744-749.
12. Wu M, He Y, She JH, Liu GP,. Delay-dependent criteria for robust stability of time-varying delay systems. Automatica 2004; 40 (8): 1435-1439.
13. He Y, Wang QG, Lin C, Wu M,. Delay-range-dependent stability for systems with time-varying delay. Automatica 2007; 43 (2): 371-376. (Pubitemid 46037586)
14. Gu K,. Discretized LMI set in the stability problem of linear uncertain time-delay systems. International Journal of Control 1997; 68 (4): 923-934.
15. Gu K,. Generalized discretization scheme of Lyapunov functional in the stability problem of linear uncertain time-delay systems. International Journal of Robust and Nonlinear Control 1999; 9 (1): 1-14.
16. Fridman E,. Descriptor discretized Lyapunov functional method: analysis and design. IEEE Transactions on Automatic Control 2006; 51 (6): 890-897. (Pubitemid 43792659)
17. Åiljac DD, StipanoviÄ DM,. Robust stabilization of nonlinear systems: the LMI approach. Mathematical Problems in Engineering 2000; 6 (5): 461-493.
18. â control for linear systems with interval time-varying delay. Automatica 2005; 41 (12): 2099-2106. (Pubitemid 41525668)
19. â control of systems with uncertainty. Automatica 2005; 41 (6): 999-1007. (Pubitemid 40556809)
20. Hale JC, Verduyn Lunel SM,. Introduction of Functional Differential Equations. Springer: New York, 1993.
21. Zhang W, Branicky MS, Phillips SM,. Stability of networked control systems. IEEE Control Systems Magazine 2001; 21 (1): 84-99. (Pubitemid 32869524)
22. Park H, Kim Y, Kim D, Kwon W,. A scheduling method for network based control systems. IEEE Transactions on Control Systems Technology 2002; 10 (3): 318-330. (Pubitemid 34630810)
23. Kim DS, Lee YS, Kwon WH, Park HS,. Maximum allowable delay bounds of networked control systems. Control Engineering Practice 2003; 11 (11): 1301-1313. (Pubitemid 37481822)
24. Naghshtabrizi P, Hespanha JP, Teel AR,. Stability of infinite-dimensional impulsive systems with application to network control systems. Proceedings of the American Control Conference, NY, U.S.A., 2007; 4899-4904.
25. Peng C, Tian YC, Tadé MO,. State feedback controller design of networked control systems with interval time-varying delay and nonlinearity. International Journal of Robust and Nonlinear Control 2008; 18 (12): 1285-1301.
26. Jiang X, Han QL,. New stability criteria for linear systems with interval time-varying delay. Automatica 2008; 44 (10): 2680-2685.