Stability and Stabilization of Discrete-Time T–S Fuzzy Systems With Stochastic Perturbation and Time-Varying Delay

This paper is concerned with the problems of stability analysis and stabilization for a class of discrete-time Takagi-Sugeno (T-S) fuzzy systems with stochastic perturbation and time-varying state delay. By means of the delay-partitioning method and slack variables, a novel fuzzy Lyapunov-Krasovskii function is constructed to reduce the conservatism of stability conditions. Those conditions are converted to finite linear matrix inequalities, which can be readily solved by standard numerical software. Then, the delay-dependent stabilization approach, which is based on a nonparallel distributed compensation scheme, is introduced for the closed-loop fuzzy systems. Finally, illustrative examples are provided to illustrate the feasibility and effectiveness of the proposed methods.