Constrained Control of Discrete-Time Positive Systems with Delays

This paper addresses controller design for discrete-time positive systems with multiple delays. The control is under positivity boundedness constraints, which means that the resulting closed-loop systems are not only stable, but also positive and bounded by a given boundary, if the initial condition is bounded. The contribution lies in two aspects. First, two necessary and sufficient conditions are established, determining whether the trajectory of a positive system can be bounded by a given boundary, provided that the initial condition is bounded. Second, two necessary and sufficient condition are provided for bounded control. 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.