On delay-dependent stability for a class of discrete nonlinear stochastic systems

IFAC Proceedings Volumes (IFAC-PapersOnline)

Volumn 16, Issue , 2005, Pages 99-104

  Rodkina, Alexandra ^a   Basin, Michael ^b  

^a UNIVERSITY OF THE WEST INDIES   (Jamaica)

^b UNIVERSIDAD AUTÓNOMA DE NUEVO LEÓN   (Mexico)

Author keywords

Asymptotic stability; Discrete stochastic time delay system; Lyapunov krasovskii and degenerate functionals; Martingale convergence theorems

Indexed keywords

ASYMPTOTIC STABILITY; DELAY CONTROL SYSTEMS; SYSTEM STABILITY;

DELAY-DEPENDENT STABILITY; FUNCTIONALS; GLOBAL ASYMPTOTIC STABILITY; LIPSCHITZ CONDITIONS; LYAPUNOV-KRASOVSKII; MARTINGALE CONVERGENCE THEOREM; NON-LINEAR STOCHASTIC SYSTEMS; STOCHASTIC TIME DELAY SYSTEM;

STOCHASTIC SYSTEMS;

EID: 79960742919     PISSN: 14746670     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.3182/20050703-6-cz-1902.00369     Document Type: Conference Paper

References (23)

1. Boukas, E.-K. and Z.-K. Liu (2002). Deterministic and Stochastic Time-Delay Systems. Birkhauser.
2. Fridman, L., A. Polyakov and P. Acosta (2001). Robust eigenvalue assignment for uncertain delay control systems. In: Proc. 3rd IFAC Workshop on Time Delay Systems. pp. 239-244. Elsevier.
3. Gu, K. and Q.-L. Han (2001). A revisit of some delay-dependent stability criteria for uncertain time-delay systems. In: Proc. 3rd IFAC Workshop on Time Delay Systems. pp. 153-158. Elsevier.
4. Gu, K. and S.-I. Niculescu (2003). Survey on recent results in the stability and control of time-delay systems. ASME Transactions. J. of Dynamic Systems, Measurement, and Control 125, 158-165.
5. Hale, J. K. and S. M. Verduyn-Lunel (1993). Introduction to Functional Differential Equations. Springer. New York.
6. Kesten, H. (1973). Random difference equations and renewal theory for the product of random matrices. Acta Math. 131, 207-248.
7. Kharitonov, V. (1999). Robust stability analysis of time-delay systems: a survey. Annual Reviews in Control 23, 185-196.
8. Kharitonov, V. and D. Melchor-Aguilar (2000). On delay-dependent stability conditions. Systems and Control Letters 40, 71-76.
9. Kolmanovskii, V. B. and A. D. Myshkis (1992). Applied Theory of Functional Differential Equations. Kluwer. Dordrecht.
10. Kolmanovskii, V. B. and V. R. Nosov (1986). Stability of Functional Differential Equations. Academic Press. London.
11. Kolmanovskii, V. B., T. L. Maizenberg and J.-P. Richard (2003). Mean square stability of difference equations with a stochastic delay. Nonlinear Analysis 52, 795-804.
12. Liao, X. and X. Mao (2000). Exponent stability of stochastic delay interval systems. Systems and Control Letters 40, 171-181.
13. Liptser, R. S. and A. N. Shiryayev (1989). The Martingale Theory. Kluwer. Dordrecht.
14. Mao, X., N. Koroleva and A. Rodkina (1998). Robust stability of uncertain stochastic differential delay equations. Systems and Control Letters 35, 325- 336.
15. Melnikov, A.V. and A.E. Rodkina (1993). Martingale approach to the procedures of stochastic approximation. Frontiers in Pure and Applied Probability 1, 165-182.
16. Niculescu, S. (2001). Delay Effects on Stability: A Robust Control Approach. Springer. Heidelberg.
17. Orlov, Y., W. Perruquetti and J.-P. Richard (2002). On identifibility of linear time-delay systems. IEEE Trans. Automat. Contr. 47, 1319-1324.
18. Richard, J.-P. (2003). Time-delay systems: an overview of some recent advances and open problems. Automatica 39, 1667-1694.
19. Rodkina, A.E. and V.R. Nosov (2003). On stability of some nonlinear scalar differential equations. Dynamic Systems and Applications 12, 285-294.
20. Rodkina, A.E., X. Mao and V.B. Kolmanovskii (2000). On asymptotic behavior of solutions of stochastic difference equations with volterra-type main term. Stochastic Analysis and Applications 18, 837-857.
21. Spreji, P. (2003). Recursive approximate maximum likehood estimation for a class of counting process models. Journal of Multivariate Analysis 39, 236-245.
22. ∞ control for uncertain stochastic systems with state delay. IEEE Trans. Automat. Contr. 47, 2089-2094.
23. Xie, S. and L. Xie (2000). Stabilization of a class of uncertain large-scale stochastic systems with time delays. Automatica 36, 161-167.