In this paper, the H-infinity control problem for descriptor systems is studied. Necessary and sufficient conditions are derived for the solution to this problem, expressed in terms of two generalised algebraic Riccati equations which may be considered to be the generalisations of the Riccati equations obtained by Doyle et al, (1989). When these conditions hold. state space formulae for a controller solving the problem is also given. The approach used in this paper is based on a generalised version of bounded real lemma, thus the proofs given are simple.