This paper studies the H-infinity filtering problem for a class of discrete-time two-dimensional (2-D) switched systems. The 2-D systems under consideration are described by the well-known Fornasini-Marchesini local state-space model. Our attention is focused on designing a full-order filter such that the filtering error system is guaranteed to be asymptotically or exponentially stable with a prescribed H-infinity disturbance attenuation level. Based on the switched quadratic Lyapunov function and the piecewise Lyapunov function approach, sufficient conditions are established to ensure the existence of the desired filters for such systems under the arbitrary switching and restricted switching signals, respectively. Furthermore, the notion of time instant for 2-D switched systems is introduced and the extended average dwell time technique is utilized under the restricted switching signal. Then the corresponding filter is designed by dealing with a convex optimization problem that can be efficiently solved via standard numerical algorithms. Finally, two numerical examples are provided to demonstrate the effectiveness of the developed filter design algorithms. (C) 2018 Elsevier Ltd. All rights reserved.