On the stabilization of a class of periodic positive discrete time systems

This paper investigates the stabilizability of a class of linear periodic discrete-time systems for which the state vector complies with a positivity constraint. LMI-based conditions for the existence of a desired periodic state feedback controller guaranteeing the resultant closed-loop system is asymptotically stable and positive are presented. The obtained results are then extended to the problem of stabilizability and positivity of linear periodic system in presence of polytopic parameter uncertainty. Numerical examples are provided to illustrate the proposed conditions.