Abstract
The asymptotic stability of Takagi–Sugeno (T–S) fuzzy systems with state delay is studied. The aim is not only to extend the fuzzy weighting-dependent Lyapunov function method for delay-free fuzzy systems to time-delay fuzzy systems, but also to provide state-of-the-art stability analysis methods for time-delay fuzzy systems. First, the fuzzy weighting-dependent Lyapunov–Krasovskii functional is used to reduce the conservatism entailed in previous results using quadratic Lyapunov–Krasovskii functionals. By adopting a recent technique called the free-weighting matrix method, a delay-dependent stability condition that improves existing results for time-delay fuzzy systems is derived. Next, an augmented fuzzy weighting-dependent Lyapunov–Krasovskii functional is proposed to further reduce the conservatism. Delay-independent stability criteria are easy corollaries of the present delay-dependent results. Finally, three examples are given to illustrate the reduced conservativeness achieved by the proposed methods.
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