This paper investigates the H₂ control problem for a class of discrete-time two-dimensional (2D) switched systems represented by a model of Roesser type. By using a multiple Lyapunov function method, sufficient conditions for evaluation of the H₂ performance for the 2D switched systems are presented in terms of linear matrix inequalities. Based on the obtained results, an H₂ output feedback controller design scheme is developed for the discrete-time 2D switched systems. A numerical example is included to demonstrate the effectiveness of the proposed method.