Improved Admissibility Analysis of Takagi–Sugeno Fuzzy Singular Systems With Time-Varying Delays

This article investigates the admissibility analysis for Takagi–Sugeno fuzzy singular systems (T–S FSSs) with time-varying delays. First, according to the decomposed state vectors, a state decomposition Lyapunov–Krasovskii functional (LKF) is constructed, which possesses fewer decision variables. And, the LKF is augmented by considering more features of the second-order Bessel–Legendre inequality (BLI). Then, the second-order BLI and the generalized reciprocally convex matrix inequality are employed to dispose the derivative of the LKF, where the $d^{2}(t)$ -dependent term exists. Meanwhile, by setting an adjustable parameter, the $d^{2}(t)$ -dependent term of the condition is handled by a relaxed quadratic function negative-determination condition. As a result, a less conservative admissibility criterion for T–S FSSs is obtained. And, the relationship between the conservatism and the numerical burden is better considered. Finally, a numerical example is given to demonstrate the reduced conservatism and computational complexity.