In this paper we investigate the stabilization problem for a class of switched affine systems with a state-dependent switching law. Since the states measurements are in general subject to perturbations and noises, we propose a robust switching law design method. Qualitative conditions for the stability of the closed-loop switched system are given. Stability conditions are also formulated as Linear Matrix Inequalities (LMIs) in order to allow numerical implementations. Results are illustrated by numerical examples in order to show the efficiency of the method and its limits.