Non-fragile dynamic output feedback control for linear systems with time-varying delay

This paper is devoted to the problems of non-fragile H _infin and L ₂-L _infin control for a class of linear systems with time-varying state delay. The purpose is to design a dynamic output feedback controller with additive gain variations such that the closed-loop system is asymptotically stable while satisfying a prescribed H _infin (or L ₂-L _infin) performance level. By using linear matrix inequality approach, a delay-dependent stability criterion is obtained by introducing a new type of Lyapunov-Krasovskii functional. Based on the obtained criterion, sufficient conditions for the existence of desired controllers are derived, and the corresponding stabilisation dynamic output feedback controller design algorithm is proposed. Numerical examples are included to illustrate the benefit and effectiveness of the proposed method.