## 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.

### MSC:

 93B12 Variable structure systems 60J75 Jump processes (MSC2010) 93C10 Nonlinear systems in control theory

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