This paper proposes a state-feedback stabilization strategy for discrete-time switched linear systems, where the switching rule and the feedback gains are designed simultaneously. The synthesis conditions are based on Lyapunov-Metzler (LM) inequalities and, contrarily to the LM or convex combination based strategies from the literature that use exhaustive search on the scalar parameters, relaxations on the stability conditions and an iterative procedure based on linear matrix inequalities are proposed to search for the scalar parameters and the matrices that solve the LM inequalities. Numerical experiments illustrate the better results obtained with the proposed approach when confronted with convex combination or LM based techniques (at the price of increasing the computational costs), being also competitive when compared with periodic switching approaches.