Under some rank condition, a new version of bounded real lemma, which is expressed
in terms of an admissible solution of a generalized discrete-time algebraic Riccati equation
(GDARE) rather than inequality, is presented for linear discrete-time descriptor systems. When
a linear discrete-time descriptor system is admissible, with the H∞-norm of its transfer matrix
less than a prescribed positive number γ, a constructive procedure is also given to obtain an
admissible solution of the above-mentioned GDARE.