Exponential stability of a class of singularly perturbed stochastic time-delay systems with impulse effect

Nonlinear Analysis: Real World Applications

Volumn 11, Issue 5, 2010, Pages 3463-3478

  Chen, Wu Hua ^a   Chen, Fu ^a   Lu, Xiaomei ^a  

^a GUANGXI UNIVERSITY   (China)

Author keywords

Exponential stability in mean square; Impulsive systems; Singular perturbations; Stochastic systems; Time delay

Indexed keywords

COMPARISON PRINCIPLE; EXPONENTIAL STABILITY; EXPONENTIAL STABILITY IN MEAN SQUARE; IMPULSE EFFECT; IMPULSIVE SYSTEMS; LYAPUNOV; SINGULAR PERTURBATIONS; SINGULARLY PERTURBED; STOCHASTIC TIME DELAY SYSTEM; SUFFICIENT CONDITIONS; TIME-SCALE DECOMPOSITION;

DELAY CONTROL SYSTEMS; EXPONENTIAL FUNCTIONS; PERTURBATION TECHNIQUES; STOCHASTIC SYSTEMS; TIME DELAY;

SYSTEM STABILITY;

EID: 77955510148     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2009.12.007     Document Type: Article

References (25)

1. A. Saberi, and H.K. Khalil Quadratic-type Lyapunov functions for singularly perturbed systems IEEE Trans. Automat. Control 29 1984 542 550
2. M. Corless, and L. Glielmo On the exponential stability of singularly perturbed systems SIAM J. Control Optim. 30 1992 1338 1360
3. P.D. Christofides, and A.R. Teel Singular perturbations and input-to-state stability IEEE Trans. Automat. Control 41 1996 1645 1650
4. L. Socha Exponential stability of singularly perturbed stochastic systems IEEE Trans. Automat. Control 45 2000 576 580
5. D.W. Luse Multivariable singularly perturbed feedback systems with time delay IEEE Trans. Automat. Control 32 1987 990 994
6. H.D. Voulov, and D.D. Bainov Asymptotic stability of the solutions of a linear singularly perturbed system with unbounded delay J. Math. Anal. Appl. 155 1991 293 311
7. V. Glizer, and E. Fridman H ∞ control of linear singularly perturbed systems with small state delay J. Math. Anal. Appl. 250 2000 49 85
8. H. Tian The exponential asymptotic stability of singularly perturbed delay differential equations with a bounded lay J. Math. Anal. Appl. 270 2002 143 149
9. E. Fridman Effects of small delays on stability of singularly perturbed systems Automatica 38 2002 897 902
10. E. Fridman Stability of singularly perturbed differential-differences systems: A LMI approach Dyn. Contin. Discrete Impuls. Syst. 9 2002 201 212
11. X. Liu, X. Shen, and Y. Zhang Exponential stability of singularly perturbed systems with time delay Appl. Anal. 82 2003 117 130
12. W.-H. Chen, Z.-H. Guan, X. Lu, and Y. Xu Exponential stability of singularly perturbed stochastic systems with delay Dyn. Contin. Discrete Impuls. Syst. Ser. B 12 2005 701 715
13. P.S. Simeonov, and D.D. Bainov Stability of the solutions of singularly perturbed systems with impulse effect J. Math. Anal. Appl. 136 1988 575 588
14. P.S. Simeonov, and D.D. Bainov Exponential stability of the solutions of singularly perturbed systems with impulse effect J. Math. Anal. Appl. 151 1990 462 487
15. W. Zhu, D. Xu, and C. Yang Exponential stability of singularly perturbed impulsive delay differential equations J. Math. Anal. Appl. 328 2007 1161 1172
16. S. Wu, D. Han, and X. Meng p -moment stability of stochastic differential equations with jumps Appl. Math. Comput. 152 2004 505 519
17. B. Liu Stability of solutions for stochastic impulsive systems via comparison approach IEEE Trans. Automat. Control 53 2008 2128 2133
18. W.-H. Chen, J.-G. Wang, Y.-J. Tang, and X. Lu Robust H ∞ control of uncertain linear impulsive stochastic systems Internat. J. Robust Nonlinear Control 18 2008 1348 1371
19. Z. Yang, D. Xu, and L. Xiang Exponential p -stability of impulsive stochastic differential equations with delays Phys. Lett. A 359 2006 129 137 (Pubitemid 44402927)
20. J. Yang, S. Zhong, and W. Luo Mean square stability analysis of impulsive stochastic differential equations with delays IEEE Trans. Math. 216 2008 474 483
21. L. Xu, and D. Xu P -attracting and p -invariant sets for a class of impulsive stochastic functional differential equations Comput. Math. Appl. 57 2009 54 61
22. W.-H. Chen, and W.X. Zheng Global exponential stability of impulsive neural networks with variable delay: An LMI approach IEEE Trans. Circuits Syst. I 56 2009 1248 1259
23. S. Boyd, L. EI Ghaoui, E. Feron, and V. Balakrishnan Linear Matrix Inequalities in Systems and Control Theory 1994 SIAM Philadelphia, PA
24. I. Kanellakopoulos, B.V. Kokotovic, and R. Marino An extended direct scheme for robust adaptive nonlinear control Automatica 27 1991 247 255
25. Z. Retchltiman, G. Silva, Stability analysis of singularly perturbed systems via vector Lyapunov methods, in: Proceedings of the 35th Conference on Decision and Control, 1996, pp. 580585