Stability and stabilization of positive systems with delays

This paper addresses stability analysis and controller design for discrete-time positive systems with multiple delays. The control is under positivity constraint, which means that the resulting closed-loop systems are not only stable, but also positive. The contribution lies in two aspects. First, a set of necessary and sufficient stability conditions is established for delayed discrete-time positive systems. Second, several necessary and sufficient conditions are presented for the existence of controllers under the positivity constraint. All the controllers are explicitly constructed if existent, and all the results are formulated as linear programming or linear matrix inequality problems, hence easy to be verified.