This paper deals with the stabilization of switched systems with respect to (w.r.t.) compact sets. We show that the switched system is stabilizable w.r.t. a compact set by means of a family of switched signals if and only if a certain control affine system whose admissible controls take values in a polytope is asymptotically controllable to that set. In addition we present a control algorithm that based on a family of open-loop controls which stabilizes the aforementioned control system, a model of the system and the states of the switched system, generates switching signals which stabilize the switched system in a practical sense. We also give results about the convergence and the robustness of the algorithm. (C) 2012 Elsevier Ltd. All rights reserved.