Stability and stabilization of constrained positive discrete-time periodic systems

In this paper, stability and stabilization issues of positive and periodic discrete systems with bounds on the control and on the state variable is addressed and a solution is provided. The proposed conditions are formulated as equality and inequality constraints enabling all the considered problems to be expressed, with the addition of appropriate cost function, in a linear programming framework. A linear state feedback controller is used in the stabilization problem. The results is extended to uncertain systems with a polytopic uncertainty description. Numerical examples are provided to illustrate the established results.