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A sliding mode approach to \(H_{\infty }\) synchronization of master-slave time-delay systems with Markovian jumping parameters and nonlinear uncertainties. (English) Zbl 1254.93046
Summary: In this paper, a sliding-mode approach is proposed for exponential \(H_{\infty }\) synchronization problem of a class of master-slave time-delay systems with both discrete and distributed time-delays, norm-bounded nonlinear uncertainties and Markovian switching parameters. Using an appropriate Lyapunov-Krasovskii functional, some delay-dependent sufficient conditions and a synchronization law including the master-slave parameters is established for designing a delay-dependent mode-dependent sliding mode exponential \(H_{\infty }\) synchronization control law in terms of linear matrix inequalities. The controller guarantees the \(H_{\infty }\) synchronization of the two coupled master and slave systems regardless of their initial states. Two numerical examples are given to show the effectiveness of the method.

93B12 Variable structure systems
60J75 Jump processes (MSC2010)
93C10 Nonlinear systems in control theory
LMI toolbox
Full Text: DOI
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