Stability analysis and controller design of positive linear systems subject to actuator saturation

This paper addresses the stability and stabilization problems for a class of positive linear systems in the presence of saturating actuators. The objective is to give conditions of the stability, and design state feedback control laws such that the closed-loop systems is asymptotically stable and positive at the origin with a large domain of attraction. Several sufficient conditions for stabilization and positivity are derived via the Lyapunov functions method and convex analysis in both the continuous-time and the discrete-time cases, respectively. The state feedback controller design and the estimation of domain of attraction are presented by solving a convex optimization problem with LMIs constraints. A numerical example is given to show the effectiveness of the proposed methods.