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Robust $H_{\infty}$ control for a class of nonlinear discrete time-delay stochastic systems with missing measurements. (English) Zbl 1166.93319
Summary: This paper is concerned with the problem of robust $H_{\infty}$ output feedback control for a class of uncertain discrete-time delayed nonlinear stochastic systems with missing measurements. The parameter uncertainties enter into all the system matrices, the time-varying delay is unknown with given lower and upper bounds, the nonlinearities satisfy the sector conditions, and the missing measurements are described by a binary switching sequence that obeys a conditional probability distribution. The problem addressed is the design of an output feedback controller such that, for all admissible uncertainties, the resulting closed-loop system is exponentially stable in the mean square for the zero disturbance input and also achieves a prescribed $H_{\infty}$ performance level. By using the Lyapunov method and stochastic analysis techniques, sufficient conditions are first derived to guarantee the existence of the desired controllers, and then the controller parameters are characterized in terms of linear matrix inequalities. A numerical example is exploited to show the usefulness of the results obtained.

MSC:
 93B36 $H^\infty$-control 93C55 Discrete-time control systems 93C10 Nonlinear control systems 34K50 Stochastic functional-differential equations 15A39 Linear inequalities of matrices 93E03 General theory of stochastic systems
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