Delay-dependent guaranteed cost control for uncertain state-delayed systems

Abstract

This paper concerns delay-dependent guaranteed cost control via memoryless state feedback controllers for a class of linear state-delayed systems with norm-bounded time-varying parametric uncertainties. New delay-dependent conditions for the existence of the guaranteed cost controller are presented in terms of matrix inequalities for both nominal state-delayed systems and uncertain state-delayed systems. An algorithm involving convex optimization is proposed to design a controller achieving a suboptimal guaranteed cost such that the system can be stabilized for all admissible uncertainties. Through numerical examples, it is shown that the proposed method can even give a lower guaranteed cost than the delay-independent method.