This paper extends the existing results on the robust H-2 and H-infinity filtering problems with respect to polytopic uncertainty. A new structure of slack variables is introduced to provide extra free dimensions in the solution space for the H-2 and H-infinity optimization. This directly leads to performance improvement and reduction of conservativeness in the filtering solution. The method is applicable to both discrete and continuous time systems. Performance of the proposed solutions in comparison with that of the existing methods is illustrated by several examples. (c) 2006 Elsevier Ltd. All rights reserved.