On stabilityand stabilizability of positive delay systems

The stabilization problem with positivity is investigated in this note for discrete-time linear systems with time delay. A delay-independent necessary and sufficient condition is proposed in terms of linear matrix inequalities (LMTs) for the existence of desired controllers that guarantee the closed-loop system to be asymptotically stable and positive. In addition, the obtained result is further extended to more general case when the system matrices contain uncertain parameters, where a sufficient condition is obtained. The frequently used polytopic parameter uncertainty is taken into consideration. Since the conditions obtained are expressed as LMIs, which can be easily verified by using standard numerical software. A numerical example is provided to illustrate the proposed results.