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Robust \(H_{\infty }\) control for uncertain discrete stochastic time-delay systems. (English) Zbl 1157.93372

Summary: This paper deals with the problems of robust stabilization and robust \(H_{\infty }\) control for discrete stochastic systems with time-varying delays and time-varying norm-bounded parameter uncertainties. For the robust stabilization problem, attention is focused on the design of a state feedback controller which ensures robust stochastic stability of the closed-loop system for all admissible uncertainties, while for the robust \(H_{\infty }\) control problem, a state feedback controller is designed such that, in addition to the requirement of the robust stochastic stability, a prescribed \(H_{\infty }\) performance level is also required to be satisfied. A linear matrix inequality (LMI) approach is developed to solve these problems, and delay-dependent conditions for the solvability are obtained. It is shown that the desired state feedback controller can be constructed by solving certain LMIs. An example is provided to demonstrate the effectiveness of the proposed approach.

MSC:

93B36 \(H^\infty\)-control
93E20 Optimal stochastic control
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