  We obtain a general characterization of discrete-time all-pass rational
matrix functions from state-space representations. It can be employed to
address model reduction problems in the same vein of the theory developed by
Glover in the continuous-time. Besides model reduction, this characterization
is shown to be useful in a variety of contexts such as studying LMI's and
Riccati equations and especially in the factorization of all-pass functions.
The results are obtained in the most general setting, without introducing any
{\em ad hoc} assumption.
