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Zbl 1227.93124
Balasubramaniam, P.; Krishnasamy, R.; Rakkiyappan, R.
Delay-interval-dependent robust stability results for uncertain stochastic systems with Markovian jumping parameters. (English)
[J] Nonlinear Anal., Hybrid Syst. 5, No. 4, 681-691 (2011). ISSN 1751-570X

Summary: This paper is concerned with the robust stability analysis of Markovian jumping uncertain stochastic systems with interval time-varying delays. The parametric uncertainties which appear in all system matrices are assumed to be norm bounded. A new Markovian jumping matrix $P_i$ is introduced for deriving the stability results. Based on the Lyapunov stability theory and stochastic analysis technique, new improved delay-dependent robust stability criteria are derived by considering the relationship among the time-varying delay, its upper bound and their difference without ignoring any terms. Numerical examples are given to verify the effectiveness and less conservativeness of the proposed method.

MSC 2000:: *93E15 Stochastic stability
93D09 Robust stability of control systems
93E03 General theory of stochastic systems
60J75 Jump processes

Keywords: linear matrix inequality; uncertain stochastic systems; Lyapunov-Krasovskii functional; Markovian jumping parameters; interval time-varying delays

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Zentralblatt MATH Berlin [Germany]