This paper proposes a robust H-infinity filter design method for discrete-time linear parameter varying systems with the state-space model matrices depending rationally on time-varying parameters. The system is described by a difference-algebraic representation and the parameters admissible values and variations are assumed to belong to given intervals. A convex optimization approach in terms of linear matrix inequalities is devised for designing robust filters. The filter design is based on Lyapunov functions with rational dependence on the system parameters and incorporates information on available bounds on the parameters variation. The proposed method can be also applied to the design of gain-scheduled H-infinity filters. Numerical examples illustrate the effectiveness of the proposed filter design. (C) 2009 Elsevier Ltd. All rights reserved.