This paper deals with the problem of robust H-infinity filtering for discrete-time systems with Lipschitz nonlinearities and uncertain parameters. Both the cases of systems subject to either polytopic or norm-bounded parameter uncertainties are treated and it is considered that all the matrices of the system state-space model can be affected by uncertain parameters. Novel methods in terms of linear matrix inequalities are proposed for designing nonlinear filters with a general structure that ensure global exponential stability of the estimation error dynamics and a prescribed (or optimized) H-infinity performance for all admissible uncertain parameters. In the case of polytopic uncertain systems, the filter design is based on an affine uncertainty-dependent Lyapunov function. Numerical examples are presented to illustrate the effectiveness of the proposed robust H-infinity filtering methods. (C) 2019 Elsevier Ltd. All rights reserved.