Representation and Factorization of Discrete-Time Rational All-Pass Functions

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.