Robust repetitive control with saturating actuators: a LMI approach

This paper addresses the problem of tracking and rejection of periodic signals for uncertain linear systems subject to control saturation. To ensure the periodic tracking/rejection, a modified state-space repetitive control structure 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, where the presence of the repetitive controller ensures the periodic tracking/rejection. 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.