On the design of nonfragile guaranteed cost controller for a class of uncertain dynamic systems with state delays

Abstract

In this article, the nonfragile guaranteed cost control problem is studied for a class of uncertain dynamic systems with multiple time delays and controller gain variation. The multiple time-varying delays are considered. The uncertainty is nonlinear time-varying and is bounded in magnitude. For all admissible uncertainties, time delays, and controller gain variations, the problem is to design a memoryless state feedback control laws such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound of a given cost function. Several criteria for the existence of such controllers are derived using the Lyapunov method. A feature of the proposed method is that an upper bound on the guaranteed cost is minimized by solving a convex optimization problem with linear matrix inequalities. A numerical example is given to illustrate the proposed method.