On the k-switching reachability sets of single-input positive switched systems

In the paper, the k-switching reachability set R_k of a single-input positive switched system is introduced, and conditions for the chain of this sets {R_k; k isin Nopf}, to stop increasing after some finite index k are given. For the special class of positive switched systems, which commute among n single-input n-dimensional systems, sufficient conditions that ensure that the n-switching reachability set coincides with the positive orthant Ropf₊ ⁿ are given. In particular, it is proved that when the system is reachable and n = 2; 3, this is always true, namely R_n = Ropf₊ ⁿ.