Controller synthesis for constrained discrete-time switched positive linear systems

This paper investigates the controller synthesis for a class of discrete-time switched linear systems with bounds on the controls and the states. First, the synthesis of state-feedback controllers guaranteeing positivity and stability of the closed-loop system is studied for sign-restricted inputs. Also, the results can be extended to asymmetrically bounded controls and constrained states. All the derived conditions are shown as linear programming framework. In addition, a cost function is proposed to maximize the length of the box constraints on the initial state. Finally, several numerical examples illustrate the validity of the developed results.