On Constrained Stabilization of Discrete–time Linear Systems

Abstract — Recently, the concepts of (k,λ)–contractive sets and set–induced finite–time Lyapunov functions were introduced in [1]. Therein it was shown that these notions provide non–conservative tools for stability analysis of homogeneous dynamics. In this paper we employ these concepts to derive new synthesis methods for constrained stabilization of linear systems. Two classes of state–feedback control strategies are proposed, namely, periodic conewise linear control laws and periodic vertex–interpolation control laws. The benefits of these synthesis methods are demonstrated for the constrained stabilization of a DC–DC buck converter. I