Delay-dependent Guaranteed Cost Control for Uncertain Time Delay System

In this paper, we propose a delay-dependent guaranteed cost controller design method for uncertain linear systems with time delay. The uncertainty is norm bounded and time-varying. A quadratic cost function is considered as the performance measure for the given system. Based on the Lyapunov method, sufficient condition, which guarantees that the closed-loop system is asymptotically stable and the upper bound value of the closed-loop cost function is not more than a specied one, is derived in terms of Linear Matrix Inequalities(LMIs) that can be solved sufficiently. A convex optimization problem can be formulated to design a guaranteed cost controller, which minimizes the upper bound value of the cost function. Numerical examples show the activeness of the proposed method.