On controllability and reachability of switched systems with digraph-directed switchings

Controllability and reachability of a class of linear switched systems is investigated, where the switching signal cannot be chosen freely but have to be determined according to a switching digraph. Based on such a digraph, the systems are divided into two types: irreducible systems and reducible systems. For irreducible systems, necessary and sufficient criterion for controllability is established. It is also proved that in this case controllability is equivalent to reachability. As for reducible systems, only sufficient condition is established and it is shown that in this case controllability is not equivalent to reachability in general by two simple examples.