Delay-range-dependent robust H∞ control for uncertain systems with interval time-varying delays

This paper deals with the problem of delay-range-dependent robust H∞ control for uncertain systems with time-varying delays and norm-bounded parameter uncertainties. The time delay is assumed to be a time-varying continuous function belonging to a given range. Firstly, some new delay-range-dependent stability and stabilization criteria are proposed by exploiting a new Lyapunov–Krasovskii functional and by making use of novel techniques for time-delay systems. These developed results enjoy much less conservatism than the existing ones due to the introduction of some free weighting matrices and a method to estimate the upper bound of the derivative of Lyapunov functional without ignoring some useful terms that take into account information of the lower and upper bounds for the time delay. Secondly, based on the criteria obtained, a delay-range-dependent criterion for the existence of a memoryless state feedback H∞ controller that ensures asymptotic stability and a prescribed H∞ performance level of the closed-loop system for all admissible uncertainties is proposed in terms of linear matrix inequality (LMI). Numerical examples are provided to demonstrate the effectiveness and benefits of the proposed method.