Analysis and stabilization of discrete-time positive systems with input saturation

This paper is centered on the local stabilization of discrete-time positive systems subject to input saturation using a static linear feedback. To estimate the domain of attraction for systems with open-loop positivity, some sufficient criteria are proposed to construct two types of sets maintaining contractive invariance for the closed-loop system, namely hyperpyramids and hyperrectangles, which are the level sets corresponding to sum-separable and max-separable Lyapunov functions, respectively. Furthermore, these criteria are nonconservative for the single-input case. In the absence of open-loop positivity, some sufficient criteria are provided to guarantee that a hyperrectangle still maintains contractive invariance for the system. Finally, two numerical experiments are presented to demonstrate the effectiveness of the obtained results.