Stability Analysis for the Discrete-Time T-S Fuzzy System with Stochastic Disturbance and State Delay

Abstract

In this paper, we study the stability for discrete-time Takagi and Sugeno (T-S) fuzzy systems with perturbation disturbance and time delay. Stochastic delay-dependent stability criteria are derived for stochastic T-S fuzzy systems with time-invariant and time-varying delays, respectively. For the time-varying delay case, a novel fuzzy Lyapunov–Krasovskii functional (LKF) without requiring all the involved symmetric matrices to be positive definite is constructed to reduce the conservatism. These stability conditions are then represented in terms of finite linear matrix inequalities (LMIs), which can be solved efficiently by using standard LMIS optimisation techniques. Two numerical examples are given to illustrate the feasibility of the proposed method.