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.
Athanasopoulos, N., Doban, A. I., & Lazar, M. (2013). On constrained stabilization of discrete-time linear systems. In 21st Mediterranean Conference on Control & Automation (pp. 831-839). IEEE . https://doi.org/10.1109/MED.2013.6608819