Hierarchical admissibility criteria for T-S fuzzy singular systems with time-varying delay

This paper studies the admissibility analysis for Takagi-Sugeno (T-S) fuzzy singular systems with a time-varying delay. A novel Lyapunov-Krasovskii functional (LKF) approach, named a delay-interval-based piecewise Lyapunov functional, is first introduced. This LKF enables the use of distinct delay-dependent matrices for each partitioned delay subinterval, thereby providing additional information on the delay and its derivative. Secondly, a zero equation approach with delay-variation-dependent free matrices is presented to avoid the appearance of the delay-dependent quadratic function after the LKF's derivative. Subsequently, a cluster of admissibility criteria for the considered systems is derived by incorporating the Bessel-Legendre integral inequality. These criteria exhibit hierarchy, which means that the larger the number of delay-interval partitions, the less conservatism. Finally, the efficacy of the proposed methods is validated through numerical examples.