Tracking and rejection of periodic signals for discrete-time linear systems subject to control saturation

This work addresses the tracking and rejection problem of periodic signals for discrete-time linear systems subject to control saturation. To ensure the periodic tracking/rejection an internal model-based controller is considered. Based on this control structure, conditions allowing the simultaneous synthesis of a stabilising state feedback gain and an anti-windup gain are proposed. Provided that references and disturbances belong to the interior of a certain admissible set, these gains guarantee that the trajectories of the closed-loop system starting in an ellipsoidal set contract to the linearity region of the closed-loop system, where the presence of the internal model ensures the periodic tracking/rejection. To compute the gains, an LMI-based optimisation problem aiming at the maximisation of the set of admissible states and/or the set of admissible references/disturbances is proposed.