The goal of this paper is to study stabilization problem for discrete-time linear switched systems. To this end, a periodic state-feedback switching controller is considered along with the generalized periodic Lyapunov inequalities. To compute the control Lyapunov function, a bilinear matrix inequality (BMI) condition is suggested. Then, we focus on developing an iterative algorithm in order to efficiently solve the BMI condition. The algorithm is based on the iterative projection of the Lyapunov matrix onto a matrix polytope. Examples are given to illustrate the proposed design method.