Generalized piecewise linear feedback stabilizability of controlled linear switched systems

The paper consider the (closed-loop) stabilizability problem of controlled linear switched systems. It is shown that if the switching system is completely controllable then it is stabilizable. Moreover, it is shown that for these systems it can be found a closed-loop (event driven) switching strategy with suitable linear feedbacks that (weakly) stabilizes the system, i.e. the switching system is stabilizable by a generalized piecewise linear feedback. These results holds for systems where the control inputs are sign constrained, too.