This paper is concerned with stability analysis and stabilization problems for two-dimensional (2D) discrete switched systems represented by a model of Roesser type. First, sufficient conditions for the exponential stability of the 2D discrete switched system are derived via the average dwell time approach. Then, based on this result, a state feedback controller is designed to achieve the exponential stability of the corresponding closed-loop system. All the results are presented in linear matrix inequalities (LMIs) form. A numerical example is given to illustrate the effectiveness of the proposed method.