Constrained control of positive discrete-time periodic systems with delays

This paper addresses the control problem of linear periodic discrete-time systems with delays under the positivity constraint, which means that the resulting closed-loop systems are not only stable, but also positive. Linear periodic state feedback controllers are used in the stabilization problem. Necessary and sufficient conditions are established for the existance of such controllers for discrete-time periodic delayed systems. Then, sufficient conditions are proposed under the additional constraint of bounded control, which means that the control inputs and the states of the closed-loop systems are bounded. Finally, the results are extended to uncertain periodic delayed systems with a polytopic uncertainty description. Numerical examples are provided to illustrate the established results.