Robust Admissibility of Uncertain T–S Fuzzy Singular Systems with Time-Varying Delay: An Input–Output Approach

This article discusses the problems of admissibility for uncertain T–S fuzzy singular systems with time-varying delay. Firstly, a model which transforms the original system into two interconnected systems by two-term approximation of the delayed state based on small gain theorem is proposed. Then, the generalized integral inequality method is used to derive the admissibility conditions for uncertain T–S fuzzy singular systems. Moreover, to account for the generalized integral inequality, new augmented Lyapunov–Krasovskii functional is constructed with some new terms. Consequently, the developed criteria are given in terms of linear matrix inequalities “LMIs,” which provide less conservative results than some recent existing ones in the literature. Finally, numerical examples are given to demonstrate the applicability and the effectiveness of the developed method in this article.