On stability and stabilization of T-S fuzzy systems with multiple random variables dependent time-varying delay

Abstract

This paper is concerned with the problems of stability and stabilization for Takagi-Sugeno (T-S) fuzzy systems with multiple random variables dependent time-varying delay. Different from the previous works, we assume that probability distributions of delay in N intervals can be observed in advance. (N-1) Bernoulli distributed random variables are utilized to indicate which interval the time-varying delay falls into at a certain time instant. Then the original T-S fuzzy systems are transformed into a new model of T-S fuzzy systems with multiple random variables dependent time-varying delay, which includes the existed ones as its special cases. Based on the new model, an appropriate Lyapunov-Krasovskii (L-K) functional is constructed. Generalized Finsler’s lemma is introduced to avoid directly dealing with the interrelationship between these correlated random variables, and Reciprocally convex inequality is used to estimate integral terms from the infinitesimal operator of L-K functional. Less conservative stability criteria and stabilization conditions are proposed in the form of linear matrix inequalities (LMIs). Finally, two examples are given to demonstrate the effectiveness of the proposed methods.