Dissipativity Analysis and Synthesis for Discrete-Time T–S Fuzzy Stochastic SystemsWith Time-Varying Delay

This paper is concerned with the problems of dissipativity analysis and synthesis for discrete-time Takagi-Sugeno fuzzy systems with stochastic perturbation and time-varying delay. First, a novel model transformation method is introduced to pull the time-varying delay uncertainty out of the original system. Consequently, the transformed model is composed of a linear time-invariant system and a norm-bounded uncertain subsystem. By using this model transformation method combined with the Lyapunov-Krasovskii technique, sufficient conditions of the dissipativity are established. Then, a fuzzy controller is designed to guarantee the dissipative performance of the closed-loop system. Finally, three examples are presented: one shows the effectiveness of model transformation method, the second performs the comparison with alternative approaches, and the third illustrates the applicability of the proposed dissipative control methods.