Abstract

"This paper addresses the problem of tracking periodic references for uncertain linear systems subject to control saturation. Accordingly to the internal model principle, a control loop containing the modes of both the references and additive disturbances is considered. From this structure, conditions in a ""quasi"" LMI form are proposed to simultaneously compute a stabilizing state feedback gain and an anti-windup gain. Provided that the references and disturbances belong to a certain admissible set, these gains guarantee that the trajectories of the closed-loop system starting in a certain invariant ellipsoidal set contract to the linearity region of the closed-loop system, ensuring therefore the perfect reference tracking. Based on these conditions, an optimization problem aiming at the maximization of the invariant set of admissible states and/or the maximization of the set of admissible references/disturbances is proposed. Numerical examples to illustrate the method are provided. ©2009 IEEE."