Linear quadratic networked control of uncertain polytopic systems.

Abstract

This paper investigates the problem of designing robust linear quadratic regulators for uncertain polytopiccontinuous-time systems over networks subject to delays. The main contribution is to provide a procedureto determine a discrete-time representation of the weighting matrices associated to the quadratic criterionand an accurate discretized model, in such a way that a robust state feedback gain computed in the discrete-time domain assures a guaranteed quadratic cost to the closed-loop continuous-time system. The obtaineddiscretized model has matrices with polynomial dependence on the uncertain parameters and an additivenorm-bounded term representing the approximation residual error. A strategy based on linear matrix inequal-ity relaxations is proposed to synthesize, in the discrete-time domain, a digital robust state feedback controllaw that stabilizes the original continuous-time system assuring an upper bound to the quadratic cost ofthe closed-loop system. The applicability of the proposed design method is illustrated through a numericalexperiment. Copyright © 2015 John Wiley & Sons, Ltd.