Controllability implies stabilizability for switched linear systems under arbitrary switching

In this paper, the stabilization of a class of switched linear systems are studied, in which each subsystem is controllable as a linear time-invariant system and the minimal dwell time assumption is satisfied, i.e., if a subsystem is remaining active, it keeps a known period of time at least. The main contribution of this paper is an asymptotically stable state feedback design algorithm and an exponentially stable state feedback design algorithm for such systems. Our methods are constructive and do not require the search for Lyapunov function.