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 delaydependent 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 delayinterval partitions, the less conservatism. Finally, the efficacy of the proposed methods is validated through numerical examples.