The paper deals with the co-design of a control policy, composed by both the state feedback and the switching control law, for discrete-time switched linear systems. Constructive conditions are given that are necessary and sufficient for the stabilizability of systems which are periodic stabilizable. The conditions are in form of a Linear Matrix Inequality (LMI) problem whose solution provides the switching law and a family of state feedback gains stabilizing the system as well as a bound on the exponential decreasing rate. The effectiveness of the proposed technique is illustrated by comparison with results from the literature. (C) 2017 Elsevier Ltd. All rights reserved.