Improved Results on Delay-Dependent $$H_\infty $$ H ∞ Control for Uncertain Systems with Time-Varying Delays

Abstract

This paper deals with the problem of delay-dependent robust $$H_\infty $$Hź control for uncertain systems with time-varying delays and norm-bounded parameter uncertainties. Firstly, some new delay-dependent stability criteria are proposed by exploiting a new Lyapunov---Krasovskii functional and free-weighting matrices method. Secondly, based on the criteria obtained, a delay-dependent criterion for the existence of a memoryless state feedback $$H_\infty $$Hź controller that ensures asymptotic stability and a prescribed $$H_\infty $$Hź performance level of the closed-loop system for all admissible uncertainties is proposed in terms of linear matrix inequalities (LMIs). These developed results enjoy much less conservatism than the existing ones due to the introduction of delay segmentation approach to estimate the upper bound of the derivative of Lyapunov functional without ignoring some useful terms that take into account information of the time-delay. Finally, numerical examples are provided to demonstrate the effectiveness and benefits of the proposed method.