Reachability and stabilizability for positive nonlinear systems on time scales

Abstract

Positive reachability of a positive system on a time scale means that system trajectories starting from the origin can reach all the points of the nonnegative cone. Positive stabilization of such a system means feedback stabilization that preserves positivity of the system. It is shown that if a positive (linear or nonlinear) continuous-time system is positively reachable from the origin, then it is positively feedback stabilizable. On the other hand, such implication does not hold in general for systems on discrete time scales, even linear ones, though it holds for one-dimensional systems. These differences between continuous-time and discrete-time systems follow from different characterizations of positive reachability for these two classes of systems.