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Sliding mode control for a class of nonlinear discrete-time networked systems with multiple stochastic communication delays. (English) Zbl 1233.93019

Summary: In this article, a Sliding Mode Control (SMC) problem is studied for a class of uncertain nonlinear networked systems with multiple communication delays. A sequence of stochastic variables obeying Bernoulli distribution is applied in the system model to describe the randomly occurring communication delays. The discrete-time system considered is also subject to parameter uncertainties and state-dependent stochastic disturbances. A novel discrete switching function is proposed to facilitate the sliding mode controller design. Sufficient conditions are derived by means of the Linear Matrix Inequality (LMI) approach. It is shown that the system dynamics in the specified sliding surface is robustly exponentially stable in the mean square if two LMIs with an equality constraint are feasible. A discrete-time SMC controller is designed that is capable of guaranteeing the discrete-time sliding-mode reaching condition of the specified sliding surface. Finally, a simulation example is given to show the effectiveness of the proposed method.

MSC:

93B12 Variable structure systems
93C55 Discrete-time control/observation systems
93C10 Nonlinear systems in control theory
93D20 Asymptotic stability in control theory
93E15 Stochastic stability in control theory
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