On constrained stabilization of discrete-time linear systems

The concepts of controlled (k, λ)-contractive sets and set-induced finite-time control Lyapunov functions are introduced in this paper. These tools are then employed 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.