Delay-dependent H∞ control of linear systems with time-varying delays using proportional-derivative state feedback

Abstract

This paper considers H∞ control problem for input-delayed systems for time-varying delays. A proportional-derivative state feedback control law is used in this paper. By this means, the resulting closed-loop system turns into a specific time-delay system of neutral type. The significant specification of this neutral system is that its delayed term coefficients depend on the controller parameters. This condition provides new challenging issues in theoretical research as well as providing new applications. In the present paper, new delay-dependent sufficient condition is derived for the existence of H∞ controller in terms of matrix inequalities, in presence of varying time-delays. The resulting H∞ controller guarantees asymptotic stability of the closed-loop system as well as a guaranteed limited system induced norm smaller than a prescribed level. Numerical examples are presented to illustrate the effectiveness of the proposed method.