On delay-dependent stability for vector nonlinear stochastic delay-difference equations with Volterra diffusion term

Systems and Control Letters

Volumn 56, Issue 6, 2007, Pages 423-430

  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 vector stochastic nonlinear time delay system

Indexed keywords

ASYMPTOTIC STABILITY; CONVERGENCE OF NUMERICAL METHODS; NONLINEAR SYSTEMS; STOCHASTIC CONTROL SYSTEMS;

DISCRETE VECTOR STOCHASTIC NONLINEAR TIME-DELAY SYSTEM; LIPSCHITZ CONDITIONS; NONLINEAR DRIFT FUNCTIONS; NONLINEAR STOCHASTIC SYSTEMS;

DIFFERENCE EQUATIONS;

EID: 34047247381     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sysconle.2006.11.001     Document Type: Article

References (24)

1. Boukas E.-K., and Liu Z.-K. Deterministic and Stochastic Time-Delay Systems (2002), Birkhauser, Basel
2. Fridman L., Polyakov A., and Acosta P. Robust eigenvalue assignment for uncertain delay control systems. Proceedings of the Third IFAC Workshop on Time Delay Systems (2001), Elsevier, Amsterdam 239-244
3. Gu K., and Han Q.-L. A revisit of some delay-dependent stability criteria for uncertain time-delay systems. Proceedings of the Third IFAC Workshop on Time Delay Systems (2001), Elsevier, Amsterdam 153-158
4. Gu K., and Niculescu S.-I. Survey on recent results in the stability and control of time-delay systems. ASME Trans. J. Dynamic Systems Measurement Control 125 (2003) 158-165
5. Hale J.K., and Verduyn-Lunel S.M. Introduction to Functional Differential Equations (1993), Springer, New York
6. Kesten H. Random difference equations and renewal theory for the product of random matrices. Acta Math. 131 (1973) 207-248
7. Kharitonov V. Robust stability analysis of time-delay systems: a survey. Annu. Rev. Control 23 (1999) 185-196
8. Kharitonov V., and Melchor-Aguilar D. On delay-dependent stability conditions. Systems Control Lett. 40 (2000) 71-76
9. Kolmanovskii V.B., Maizenberg T.L., and Richard J.-P. Mean square stability of difference equations with a stochastic delay. Nonlinear Anal. 52 (2003) 795-804
10. Kolmanovskii V.B., and Myshkis A.D. Applied Theory of Functional Differential Equations (1992), Kluwer Academic Publisher, Dordrecht
11. Kolmanovskii V.B., and Nosov V.R. Stability of Functional Differential Equations (1986), Academic Press, London
12. Liao X., and Mao X. Exponent stability of stochastic delay interval systems. Systems Control Lett. 40 (2000) 171-181
13. Liptser R.S., and Shiryayev A.N. The Martingale Theory (1989), Kluwer Academic Publisher, Dordrecht
14. Mao X., Koroleva N., and Rodkina A. Robust stability of uncertain stochastic differential delay equations. Systems Control Lett. 35 (1998) 325-336
15. Melnikov A., and Rodkina A. Martingale approach to the procedures of stochastic approximation. Frontiers Pure Appl. Probab. 1 (1993) 165-182
16. Niculescu S. Delay Effects on Stability: A Robust Control Approach (2001), Springer, Heidelberg
17. Richard J.-P. Time-delay systems: an overview of some recent advances and open problems. Automatica 39 (2003) 1667-1694
18. Rodkina A., and Basin M. On delay-dependent stability for a class of nonlinear stochastic delay-differential equations. Math. Control Signals Systems 18 (2006) 187-197
19. Rodkina A.E., and Mao X. On boundedness and stability of solutions of nonlinear difference equation with nonmartingale type noise. J. Differential Equations Appl. 7 (2001) 529-550
20. Rodkina A., Mao X., and Kolmanovskii V. On asymptotic behavior of solutions of stochastic difference equations with volterra-type main term. Stochastic Anal. Appl. 18 (2000) 837-857
21. Rodkina A., and Nosov V. On stability of some nonlinear scalar differential equations. Dynamic Systems Appl. 12 (2003) 285-294
22. Spreji P. Recursive approximate maximum likelihood estimation for a class of counting process models. J. Multivariate Anal. 39 (2003) 236-245
23. Xie S., and Xie L. Stabilization of a class of uncertain large-scale stochastic systems with time delays. Automatica 36 (2000) 161-167
24. ∞ control for uncertain stochastic systems with state delay. IEEE Trans. Automat. Control. 47 (2002) 2089-2094