Admissibility Analysis of T-S Fuzzy Time Delay Descriptor Systems via Symmetric L-K Functionals

Existing approaches for admissibility analysis of T-S fuzzy descriptor time delay systems fail to balance conservatism reduction and computational complexity. This paper proposes a low-conservatism analysis and stabilization method based on the symmetric Lyapunov–Krasovskii (L-K) functional. By exploiting the boundedness of membership function derivatives, and combining Jensen’s integral inequality with auxiliary slack matrices to achieve tight bounding of nonlinear terms, we derive an admissibility criterion for open-loop systems with significantly reduced conservatism. A well-suited L-K functional is constructed targeting the structural characteristics of fuzzy singular matrices Eξ, a state feedback controller is designed via the parallel distributed compensation (PDC) strategy, and solvable sufficient conditions for the admissibility of closed-loop systems are established. Numerical examples demonstrate that the maximum allowable delay upper bound obtained by the proposed method outperforms that of existing state-of-the-art approaches while balancing conservatism and computation cost and verifying the superiority of the proposed method.