Control of uncertain state-delay systems: Guaranteed cost approach

Abstract

In this paper, we address the problems of robust performance analysis and control synthesis for a class of linear continuous-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 appropriate notions of robust stability independent of delay and delay dependent. In both cases, we show that the adopted notion guarantees an upper bound on a linear quadratic cost function. For the 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 Riccati or linear matrix inequalities.