Admissibility and stabilization of descriptor T–S fuzzy systems with two additive time-varying delays

This paper discusses the problems of admissibility and stabilization of descriptor T–S fuzzy systems with two additive time-varying delays. Firstly, new delay-dependent conditions are derived by applying a generalized free matrix based on Bessel–Legendre inequality, by constructing an appropriate Lyapunov–Krasovskii functional and by introducing some slack variables in order to reduce the conservatism and to give more relaxation to the considered system. Then, and based on the established admissibility conditions, a fuzzy controller criterion is designed to ensure the regularity, the impulse-free, and the asymptotic stability of the descriptor T–S fuzzy systems with time-varying delay. All the proposed conditions and criteria are expressed in terms of linear matrix inequalities. Finally, some numerical and practical examples are provided to demonstrate the effectiveness and the applicability of the proposed method and to compare the obtained results with some existing ones in the literature.