In this report, H∞ control problem for discrete-time descriptor systems is studied. Necessary and sufficient conditions are derived for the solution to this problem expressed in terms of two generalized discrete-time algebraic Riccati equations which may be considered to be the generalizations of the Riccati equations obtained by Doyle et al.(1989), Iglesias and Glover(1991), and Wang et al.(1998).When these conditions hold, state space formulae for controllers solving the problem are also given. The approach used in this report is based on a generalized version of discrete-time Bounded Real Lemma.