Robust Exponential Stability of a Class of Uncertain Switched Fuzzy Systems

This paper focuses on the problem of the exponential stability for a class of uncertain switched fuzzy (SF) delay systems. A switching control strategy is presented for a class of uncertain SF delay systems. A switched fuzzy delay system, which differs from existing ones, can often describe more precisely the fuzzy, continuous dynamics and discrete dynamics as well as their coupling and interactions in complex engineering systems. Firstly, a class of uncertain switched fuzzy delay systems is given, and in this class model the switched parallel distributed compensation controller is introduced. Next, using the scheme of average dwell time, the multiple Lyapunov function method is adopted to establish the stability results for this class of SF systems. Moreover, sufficient conditions for exponential stability are presented and stabilizing switching law is designed. A bound on the average dwell time guaranteeing exponentially stability of SF delay systems can be explicitly calculated via the solutions of some linear matrix inequalities (LMIs). Finally, two simulations of various comparisons for the elaborated examples demonstrate the feasibility and the effectiveness of the proposed method.