Sliding Mode based Fuzzy Control of Stochastic Systems with Time Delay

Abstract

This paper focuses on the design of a fuzzy sliding mode controller for stochastic time-delay systems with unknown nonlinearities. The Takagi-Sugeno (T-S) fuzzy model is generalized to describe the stochastic delay system. A sufficient condition is derived such that the sliding mode dynamics is mean-square exponentially stable in the specified switching surface. Then, a sliding mode based control law is synthesized to guarantee the reachability of the specified sliding surface. The stability criterion is formulated by linear matrix inequalities and dependent on the size of time delay. Therefore, the result developed is less conservative than some existing results