Stabilization for discrete-time interval switched positive linear systems

In our investigation, both fast switching and slow switching-the arbitrary switching and the average dwelltime switching are considered, and the original system is not necessarily to be positive. In each switching case, we derive a sufficient condition for the existence of a set of state-feedback controllers guaranteeing the positivity and stability of the closed-loop system for all admissible interval uncertainties. All the obtained sufficient conditions are formulated in terms of linear inequalities, thus the desired controller parameters can be conveniently determined by solving a simple linear programming problems. A numerical example is given to illustrate the effectiveness and the potential of the proposed approach.