Guaranteed cost control of uncertain discrete systems with delays

In this paper, we address the problems of robust performance analysis and control synthesis for a class of discrete-time systems with parameter uncertainty and unknown state-delay. The parameter uncertainty is real time-varying norm-bounded and the state-delay is a constant within a prescribed interval. For the robust performance analysis problem, we adopt an appropriate notion of robust stability for discrete-time uncertain time-delay systems and show that this notion guarantees an upper bound on a linear quadratic cost function. For the control synthesis problem, we show that a robust state-feedback controller can be constructed to render the closed-loop system robustly stable while guaranteeing a prescribed level of performance. The developed results are expressed in terms of algebraic matrix inequalities. A numerical example is presented to illustrate the theory.