Equivalence of some controllability notions for linear switched systems and their geometric criteria

In this paper, the hybrid controllability and mode controllability of switched linear systems are investigated. It is proved that, for switched linear systems, the hybrid controllability is equivalent to the state controllability. Based on this fact, a sufficient and necessary condition for hybrid controllability of switched linear systems is established. Furthermore, the results are extended to switch linear systems with time-delay in control. Two examples are provided to illustrate our results.