An LMI approach to guaranteed cost control of linear uncertain time-delay systems

Abstract

The guaranteed cost control problem via memoryless state feedback controllers is studied in this paper for a class of linear time-delay systems with norm-bounded time-varying parametric uncertainty and a given quadratic cost function. Sufficient conditions for the existence of guaranteed cost controllers are given in terms of linear matrix inequalities (LMIs). Furthermore, a convex optimization problem with LMI constraints is formulated to design the optimal guaranteed cost controller which minimizes the guaranteed cost of the closed-loop uncertain system.