This paper investigates the state feedback H ∞ stabilization problem for a class of discrete-time 2D (two-dimensional) switched systems represented by a model of Roesser type. First, sufficient conditions for the asymptotical stability and H ∞ disturbance attenuation performance of the underlying system are derived via common Lyapunov function approach and multiple Lyapunov function approach, respectively. Then, based on the obtained stability results, two state feedback controller design methods are proposed to guarantee that the resulting closed-loop system is asymptotically stable and achieves a prescribed disturbance attenuation level γ. Finally, two numerical examples are provided to verify the effectiveness of the proposed methods.