On the reachability properties of continuous-time positive systems

In this paper, reachability properties of continuous-time positive systems are introduced and characterized in algebraic terms. Specifically, first it is shown that reachability and strong reachability are equivalent properties, and thus the characterization of strong reachability derived in (Commault and Alamir, 2007) is extended to the weaker notion of reachability. In the second part of the paper, essential reachability is introduced, and necessary and sufficient conditions for this property to hold are provided.