Improved Admissibility Criteria for Takagi–Sugeno Fuzzy Singular Systems With Time-Varying Delay

This article studies the admissibility stability issue of Takagi–Sugeno fuzzy singular (TFS) systems with time-varying delay. First, negative-definiteness constraints for
$n$
th-order matrix-valued polynomials are established based on the Finsler's Lemma. A new reciprocally convex inequality (RCI) is developed according to the proposed negative-definiteness method. Then, an improved state decomposition Lyapunov–Krasovskii (L–K) functional is constructed based on the decomposed state method. The improved L–K functional is augmented by considering more information on TFS system states and the delay-dependent matrix. Based on the novel RCI and the L–K functional, a less conservative admissibility criterion is derived. Finally, a well-studied numerical example is performed to reveal the superiority and validity of the proposed admissibility criteria.