An LMI approach to sub-optimal guaranteed cost control for uncertain time-delay systems

Abstract

This paper presents results on the design of robust memoryless state feedback controller for uncertain time-delay systems with norm bounded uncertainty. It is proved that quadratic stabilization of uncertain time-delay systems is necessary and sufficient for the feasibility of an LMI problem. The robust state feedback controller can be constructed using the corresponding feasible solution of the LMI problem. A procedure is given to select a suitable state feedback controller that is also sub-optimal in the sense of minimizing a bound on an integral quadratic performance index.