Robust Stochastic Stabilization and Robust H8 Control for Uncertain Stochastic Fuzzy Systems

This note investigates the problems of robust stabilization and robust H_infin control for Takagi-Sugeno fuzzy systems whose parameters involve both deterministic uncertainties and stochastic uncertainties. To the end, deterministic uncertainties are assume to be time-varying norm-bounded and to appear in both the state matrices and input ones, while stochastic uncertainties are described by Ito stochastic integral. The purpose of the robust stochastic stabilization problem is to design a state feedback controller such that the closed-loop system is mean-square exponentially stable for all admissible uncertainties. In the robust H_infin control problem, in addition to robust stochastic stability requirement, a prescribed H_infin 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