This paper is concerned with the problem of robust filtering for uncertain linear discrete-time descriptor systems. The matrices of the system state-space model are uncertain, belonging to a given polytope. A linear matrix inequality based method is proposed for designing a linear stationary filter that guarantees the asymptotic stability of the estimation error and gives an optimized upper bound on the asymptotic error variance, irrespective of the parameter uncertainty. The proposed robust filter design is based on a parameter-dependent Lyapunov function, which is shown to outperform parameter-independent ones. (C) 2007 Elsevier Ltd. All rights reserved.