Constrained control of discrete-time linear periodic system

The aim of this paper is twofold. In the first part, we provide a method for constructing invariant sets for discrete-time linear periodic systems with state and input constraints. The main advantage of the method is that it generates invariant sets at any step of the underlying set iteration. In the second part a novel interpolating controller between a local unconstrained optimal control law and a global maximum state contractive controller is proposed. At each time instant, two linear programming problems are solved on-line. Proofs of recursive feasibility and asymptotic stability are given.