A piecewise analysis method to stability analysis of linear continuous/discrete systems with time-varying delay

International Journal of Robust and Nonlinear Control

Volumn 19, Issue 13, 2009, Pages 1493-1518

  Yue, Dong ^a   Tian, Engang ^a   Zhang, Yijun ^b  

^a HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b NANJING UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

Linear systems; LMI; Lyapunov functional; Stability

Indexed keywords

ANALYSIS METHOD; CORRESPONDING CRITERIA; DELAY DEPENDENT STABILITY CRITERION; DELAY-DEPENDENT STABILITY; LMI; LYAPUNOV FUNCTIONAL; LYAPUNOV FUNCTIONALS; NUMERICAL EXAMPLE; PIECE-WISE; STABILITY ANALYSIS; SUB-INTERVAL; SUBINTERVALS; TIME-VARYING DELAY;

LINEAR CONTROL SYSTEMS; LINEAR MATRIX INEQUALITIES; SYSTEM STABILITY; THREE TERM CONTROL SYSTEMS; TIME VARYING CONTROL SYSTEMS;

STABILITY CRITERIA;

EID: 69049102307     PISSN: 10498923     EISSN: 10991239     Source Type: Journal    
DOI: 10.1002/rnc.1399     Document Type: Article

References (31)

1. Basin M, Sanchez E, Martinez-Zuniga R. Optimal linear filtering for systems with multiple state and observation delays. International Journal of Innovative Computing, Information and Control 2007; 3: 1309-1320.
2. Boukas NF, Al-Muthairi EK. Delay-dependent stabilization of singular linear systems with delays. International Journal of Innovative Computing, Information and Control 2006; 2: 283-291.
3. Fridman E. New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems. Systems and Control Letters 2001; 43: 309-319.
4. Fridman E, Shaked U. H∞ control of linear state delay descriptor systems: an LMI approach. Linear Algebra and its Applications 2002; 351-352: 271-302.
5. Gao H, Lam J. New results on stability of discrete-time systems with time-varying state delay. IEEE Transactions on Automatic Control 2007; 52: 328-334.
6. Gao H, Lam J, Wang C, Wang Y. Delay-dependent output-feedback stabilization of discrete-time systems with time-varying state delay. IEE Proceedings: Control Theory and Applications 2004; 151: 691-698.
7. Gu K, Kharitonov VL, Chen J. Stability of Time-delay Systems. Brikhauser: Boston, 2003.
8. He Y, Wu M, She JH, Liu GP. Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic-type uncertainties. IEEE Transactions on Automatic Control 2004; 49: 828-832.
9. Han QL, Yue D. Absolute stability of Lur'e systems with time-varying delay. IET Control Theory 2007; 1: 854-859.
10. Mahmoud MS, Shi Y, Nounou HN. Resilient observer-based control of uncertain time-delay systems. International Journal of Innovative Computing, Information and Control 2007; 3: 407-418.
11. Park P, Ko JW. Stability and robust stability for systems with a time-varying delay. Automatica 2007; 43: 1855-1858.
12. 2-gain analysis for switched delay systems: a delay-dependent method. Automatica 2006; 42: 1769-1774.
13. Sun X, Zhao J, Wang W. Two design schemes for robust adaptive control of a class of linear uncertain neural delay systems. International Journal of Innovative Computing, Information and Control 2007; 3: 385-396.
14. Wang R, Zhao J. Exponential stability analysis for discrete-time switched linear systems with time-delay. International Journal of Innovative Computing, Information and Control 2007; 3: 1557-1564.
15. Xu SY, Lam J, Chen TW. Robust H∞ control for uncertain discrete stochastic time-delay systems. Systems and Control Letters 2004; 51: 203-215.
16. Yue D, Han Q-L. A delay-dependent stability criterion of neutral systems and its application to a partial element equivalent circuit model. IEEE Transactions on Circuits and Systems-II 2004; 51(12): 685-689.
17. Fridman E, Shaked U. A descriptor system approach to H∞ control of linear time-delay systems. IEEE Transactions on Automatic Control 2002; 47(2): 253-270.
18. Moon YS, Park P, Kwon WH. Robust stabilization of uncertain input-delayed systems using reduction method. Automatica 2001; 37: 307-312.
19. Shustin E, Fridman E. On delay-derivative-dependent stability of systems with fast-varying delays. Automatica 2007; 43: 1649-1655.
20. Chen WH, Guan ZH, Yu P. Delay-dependent stability and H∞ control of uncertain discrete-time Markovian jump systems with mode-dependent time delays. Systems and Control Letters 2004; 52: 361-376.
21. Jiang X, Han QL, Yu XH. Stability criteria for linear discrete-time systems with interval-like time-varying delay. Proceedings of the American Control Conference, New Orleans, U.S.A., 2005; 2817-2822.
22. Yue D. Robust stabilization of uncertain systems with unknown input delay. Automatica 2004; 40(2): 331-336.
23. Yue D, Han Q-L. Delayed feedback control of uncertain systems with time-varying input delay. Automatica 2005; 41(2): 233-240.
24. Yue D, Han Q-L, Lam J. Network-based robust H8excl;Ä control of systems with uncertainty. Automatica 2005; 41: 999-1007.
25. Peaucelle D, Arzelier D, Henrion D, Gouaisbaut F. Quadratic separation for feedback connection of an uncertain matrix and an implicit linear transformation. Automatica 2007; 43: 795-801.
26. He Y, Wang Q-G, Lin C, Wu M. Delay-range-dependent stability for systems with time-varying delay. Automatica 2007; 43: 371-376.
27. Jiang XF, Han QL. On H∞ control for linear systems with interval time-varying delay. Automatica 2005; 41: 2099-2106.
28. He Y, Wang QG, Xie LH, Lin C. Further improvement of free-weighting matrices technique for systems with time-varying delay. IEEE Transactions on Automatic Control 2007; 52: 293-299.
29. Wu M, He Y, She JH, Liu GP. Delay-dependent criteria for robust stability of time-varying delay systems. Automatica 2004; 40: 1435-1439.
30. Fridman E. A new Lyapunov technique for robust control of systems with uncertain non-small delays. IMA Journal of Mathematical Control and Information 2006; 23: 165-179.
31. He Y, Wu M, Liu GP, She JH. Output feedback stabilization for discrete-time systems with a time-varying delay. Proceedings of the 26th Chinese Control Conference, Zhangjiajie, China, 26-31 July 2007; 64-70.