Robust periodic reference tracking for uncertain linear systems subject to control saturations

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.