An algebraic approach to the structural properties of switched positive systems

Switched positive systems deserve investigation both for theoretical reasons and for practical applications. Indeed, switching among different system models naturally arises as a way to mathematically formalize the fact that the system laws change under different operating conditions. This is true, e.g., when resorting to compartmental models; each of them may satisfactorily capture the behavior of a physiological system only under specific working conditions, so when these conditions change the system model has to switch to a different structure. For instance, the insulin-sugar metabolism is captured by two different compartmental models: one valid in steady-state and the other which is suitable to describe the evolution under perturbed conditions, following an oral assumption or an intravenous injection. The aim of this paper is to define controllability and reachability properties for continuous time switched positive systems, and to provide some preliminary characterizations of these properties.