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Fuzzy model-based control of nonlinear stochastic systems with time-delay. (English) Zbl 1239.93035
Summary: This note investigates the problems of robust stabilization and robust ${H}_{\infty }$ control for a class of nonlinear stochastic delay systems – stochastic fuzzy delay systems. The purpose of the robust stochastic stabilization problem is the design of a state feedback controller such that the closed-loop system is mean-square exponentially stable for all admissible uncertainties. In the robust ${H}_{\infty }$ control problem, in addition, a prescribed ${H}_{\infty }$ performance is required to be archived. Sufficient conditions for the solvability of these problems are given in terms of solutions to a set of linear matrix inequalities (LMIs). The developed theory is illustrated by numerical simulation.
##### MSC:
 93B36 ${H}^{\infty }$-control 93C42 Fuzzy control systems 93D15 Stabilization of systems by feedback 93E15 Stochastic stability