Asynchronous $$H_{\infty }$$ H ∞ Control of Switched Uncertain Discrete-Time Fuzzy Systems via Basis-Dependent Multiple Lyapunov Functions Approach

Abstract

This paper first investigates robust stability of open-loop switched uncertain discrete-time fuzzy systems (SUDFSs) under mode-dependent average dwell time (MDADT) switching. By a basis-dependent multiple Lyapunov functions (BLFs) approach, which has more flexibility than the multiple quadratic Lyapunov functions approach, computable robust stability conditions are presented in terms of linear matrix inequalities (LMIs). Then, the investigation is extended to robust \(H_{\infty }\) control of closed-loop SUDFSs by using the same approach. The asynchronous state feedback \(H_{\infty }\) controllers which can stabilize the SUDFSs and guarantee weighted \(H_{\infty }\) performance are obtained by solving a set of LMIs. A numerical example and a practical example are provided to show the advantage of the proposed approach.