This paper is concerned with the robust H-2 and H-infinity filtering problems for linear discrete-time systems with polytopic parameter uncertainty. We aim to derive a less-conservative design than existing linear matrix inequality (LMI) based sufficient conditions. It is shown that a more efficient evaluation of robust H2 or H. performance can be obtained by a matrix inequality condition which contains additional free parameters as compared to existing characterizations. When applying this new matrix inequality condition to the robust filter design, these parameters provide extra degrees of freedom in optimizing the guaranteed H-2 or H-infinity performance and lead to a less-conservative design. (C) 2004 Elsevier Ltd. All rights reserved.