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Robust $\cal H_{\infty }$ sliding mode control for nonlinear stochastic systems with multiple data packet losses. (English) Zbl 1273.93147
Summary: In this paper, an $\cal H_{\infty }$ Sliding Mode Control (SMC) problem is studied for a class of discrete-time nonlinear stochastic systems with multiple data packet losses. The phenomenon of data packet losses, which is assumed to occur in a random way, is taken into consideration in the process of data transmission through both the state-feedback loop and the measurement output. The probability for the data packet loss for each individual state variable is governed by a corresponding individual random variable satisfying a certain probabilistic distribution over the interval [0 1]. The discrete-time system considered is also subject to norm-bounded parameter uncertainties and external nonlinear disturbances, which enter the system state equation in both matched and unmatched ways. A novel stochastic discrete-time 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 exponentially stable in the mean square with a prescribed $\cal H_{\infty }$ noise attenuation level if a LMI with an equality constraint is feasible. A discrete-time SMC controller is designed capable of guaranteeing the discrete-time sliding mode reaching condition of the specified sliding surface with probability 1. Finally, a simulation example is given to show the effectiveness of the proposed method.
##### MSC:
 93E03 General theory of stochastic systems 93B12 Variable structure systems 93C10 Nonlinear control systems 93B35 Sensitivity (robustness) of control systems 93C55 Discrete-time control systems
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