Controllability of switched linear systems

In this paper, the controllability of a switched linear system, which is a collection of linear time-invariant systems along with some maps for "switching" among them, is addressed. First, a controllable state set is defined as a basic tool to discuss the controllability condition. Next, it is proved that the controllability of a multi-input system is equivalent to that of a single-input system. Finally, a sufficient and necessary condition for controllability of third-order systems is presented. According to the proof of this criterion, we state a conjecture on the controllability condition of n-dimensional systems. A numeric example is given to illustrate the result.