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Robust exponential stability of stochastically nonlinear jump systems with mixed time delays. (English) Zbl 1252.93096
Summary: In this paper, the problem of robust exponential stability is investigated for a class of stochastically nonlinear jump systems with mixed time delays. By applying the Lyapunov-Krasovskii functional and stochastic analysis theory as well as matrix inequality technique, some novel sufficient conditions are derived to ensure the exponential stability of the trivial solution in the mean square. Time delays proposed in this paper comprise both time-varying and distributed delays. Moreover, the derivatives of time-varying delays are not necessarily less than 1. The results obtained in this paper extend and improve those given in the literature. Finally, two numerical examples and their simulations are provided to show the effectiveness of the obtained results.

##### MSC:
 93D09 Robust stability 93E15 Stochastic stability in control theory 93E03 Stochastic systems in control theory (general) 60J75 Jump processes (MSC2010) 93C10 Nonlinear systems in control theory
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