On the reachability of continuous-time positive switched systems

In this paper we address the reachability of continuous-time positive switched systems. In detail, we first provide the reachability definition and a necessary condition for its existence. We then fully explore the “pattern reachability” problem, namely the problem of reaching, for every subset S of {1, 2, . . . , n}, at least one nonnegative state vector whose nonzero entries are exactly those corresponding to the elements of S. Finally, for the class of n-dimensional singleinput systems switching among n subsystems, necessary and sufficient conditions for reachability are given.