Exponential stability of singularly perturbed stochastic systems with delay

Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms

Volumn 12, Issue 5-6, 2005, Pages 701-715

  Chen, Wu Hua ^a   Guan, Zhi Hong ^b   Lu, Xiaomei ^b   Xu, Yuedong ^b  

^a GUANGXI UNIVERSITY   (China)

^b HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

Exponential stability; Linear matrix inequality; Singular perturbation; Stochastic systems; Time delay systems

Indexed keywords

EID: 28744454370     PISSN: 14928760     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (15)

1. ∞ control of linear singularly perturbed systems with small state delay, J. Math. Anal. Appl., 250, (2000) 49-85.
2. E. Fridman, Effects of small delays on stability of singularly perturbed systems, Automatica, 38, (2002) 897-902.
3. E. Fridman, Stability of singularly perturbed differential-differences systems: a LMI approach. Dynamics of Continuous, Discrete and Impulsive Systems, 9, (2002) 201-212.
4. D. W. Luse, Multivariable singularly perturbed feedback systems with time delay, IEEE Trans. Automat. Contr., 32, (1987) 990-994.
5. S-T. Pan, F-H. Hsiao, and C-C.Teng, Stability bound of multiple time delay singularly perturbed systems, Electronic Letters, 32, (1996) 1327-1328.
6. C. Tang and T. Basar, Stochastic stability of singularly perturbed nonlinear systems. In Proceedings of the 40th IEEE Conference on Decision and Control, pages 399-404, 2001.
7. L. Socha, Exponential stability of singularly perturbed stochastic systems, IEEE Trans. Automat. Contr., 45, (2000) 576-580.
8. M. El-Ansary, Stochastic feedback design for a class of nonlinear singularly perturbed systems, Int. J. Syt. Sci., 22, (1991) 2013-2023.
9. M. El-Ansary and H. K. Khalil, On the interplay of singular perturbations and wide-band stochastic fluctuations, SIAM J. Contr. Optim., 24, (1986) 83-94.
10. E. Fridman, New Lyapunov-Krasovskii functional for stability of linear retard and neutral type systems, Syst. Contr. Lett., 43, (2001) 309-319.
11. ∞ control of linear time-delay systems, IEEE Trans. Automat. Contro., 47, (2002) 253-270.
12. ∞ control of linear state-delay descriptor systems, Linear Algebra and Applications, 351-352, (2002) 271-302.
13. Y. S. Moon, P. Park, W. H. Kwon, and Y. S. Lee, Delay-dependent robust stabilization of uncertain state-delayed systems, Int. J. Contr., 74, (2001) 1447-1455.
14. A. Saberi and H. K. Khalil, Quadratic-type Lyapunov functions for singularly perturbed systems, IEEE Trans. Automat. Contr., 29, (1984) 542-550.
15. M. Corless and L. Glielmo, On the exponential stability of singularly perturbed systems, SIAM J. Contr. Optim., 30, (1992) 1338-1360.