New results for T-S fuzzy systems with hybrid communication delays

Abstract

This paper deals with the stability problem of T-S fuzzy systems (TSFSs) with hybrid communication delays (HCDs). Compared with traditional communication delays, HCDs with Bernoulli distributed white noise sequences not only involve probabilistic discrete time-varying delays but also random additive time-varying delays (ATVDs). Based on the delay-product-type function (DPTF) and the second derivative method, a novel Lyapunov-Krasovskii functional (LKF) is developed, which fully considers the information of various communication delays. Moreover, by using novel integral inequalities and stochastic analysis theory, new stabilization criteria are established. Meanwhile, the desired fuzzy state feedback controller with HCDs and parallel distributed compensation (PDC) is designed by solving a set of linear matrix inequalities (LMIs). In the end, the usefulness of the obtained theoretical results is illustrated through two numerical simulation examples.