Design of switching sequences for controllability realization of switched linear systems

In this paper, we study the problem of designing switching sequences for controllability of switched linear systems. Each controllable state set of designed switching sequences coincides with the controllable subspace. Both aperiodic and periodic switching sequences are considered. For the aperiodic case, a new approach is proposed to construct switching sequences, and the number of switchings involved in each designed switching sequence is shown to be upper bounded by d(d-d1+1).d(d-d1+1). Here d   is the dimension of the controllable subspace, d1=dim∑i=1m〈Ai|Bi〉, where (Ai,Bi)(Ai,Bi) are subsystems. For the periodic case, we show that the controllable subspace can be realized within d switching periods.