This paper addresses the problem of tracking and rejection of periodic signals for linear multi-input, multi-output systems subject to control saturation. To ensure the periodic tracking/rejection, a modified state-space repetitive control structure is considered. Conditions in a "quasi" linear matrix inequality 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 ellipsoidal set contract to the linearity region of the closed-loop system, where the presence of the repetitive controller ensures the periodic tracking/rejection.