In this paper, the problem of Ho, filtering for descriptor systems with strict linear matrix inequalities (LMIs) is investigated. The necessary and sufficient conditions for the solvability and the expression of the solution are obtained for both continuous-time and discrete-time descriptor systems. The proposed continuous-time filters extend the results presented by Xu and Lam (2006) by removing semi definite conditions and introducing new formulation for the filter parameters which does not require determination of intermediate variables. For discrete-time descriptors, differing from existing methods that provide sufficient conditions only, two necessary and sufficient conditions are introduced. New proposed design methods propose less conservative results comparing with existing works. Two numerical examples are presented to demonstrate the applicability of the proposed methods. (C) 2017 Elsevier Ltd. All rights reserved.