This paper deals with stability analysis and control design of discrete-time switched linear systems. The results are based on a new sufficient condition for exponential stabilizability. A performance index that falls in the context of H2 norm is considered in order to optimize the joint design of a state dependent switching function and a state feedback control law. All control design conditions are expressed through linear matrix inequalities (LMIs). Comparisons with other available design procedures are made by means of examples borrowed from the literature. The present procedure is more amenable for control synthesis purposes and simpler from both theoretical and numerical viewpoints. Three state feedback control switching strategies are presented. The complexity of the control law is discussed Ver menos