Controllability of Switched Linear Systems

This paper considers the controllability of switched linear systems. The largest controllable subspace, C, of a switched linear system is well known [6]. This paper shows that when the system is not completely controllable, C divides the state space into 2 or 3 path-wise connected invariant sub-manifolds. Then we consider whether each path-wise connected component is a controllable sub-manifold. Certain sufficient conditions are obtained for each sub-manifold to be a controllable sub-manifold. A few examples are given to demonstrate the result.