Delay-range-dependent robust stabilization for uncertain T–S fuzzy control systems with interval time-varying delays

This paper is concerned with robust stabilization for a class of T–S fuzzy control systems with interval time-varying delays. An approach is proposed to significantly improve the system performance while reducing the number of scalar decision variables in linear matrix inequalities. The main points of the approach are: (i) two coupling integral inequalities are proposed to deal with some integral items in the derivation of the stability criteria; (ii) an appropriate Lyapunov–Krasovskii functional is constructed by including both the lower and upper bounds of the interval time-varying delays; and (iii) neither model transformation nor free weighting matrices are employed in the theoretical result derivation. As a result, some improved sufficient stability criteria are derived, and the maximum allowable delay bound and controller gains can be obtained simultaneously by solving an optimization problem. Numerical examples are given to demonstrate the effectiveness of the proposed approach.