This paper deals with the stabilization of switched affine systems. The particularities of this class of nonlinear systems are first related to the fact that the control action is performed through the selection of the switching mode to be activated and, second, to the problem of providing an accurate characterization of the set where the solutions to the system converge to. In this paper, we propose a new method based on a control Lyapunov function, that provides a more accurate invariant set for the closed-loop systems, which is composed by the union of potentially several disjoint subsets. The main contribution is presented as a non convex optimization problem, which refers to a Lyapunov-Metzler condition. Nevertheless a gridding technique applied on some parameters allows obtaining a reasonable solution through an LMI optimization. The method is then illustrated on two numerical examples that demonstrate the potential of the method.