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

In this paper, we obtain a general characterization of discrete-time all-pass rational matrix functions from state-space representations. We establish a general characterization of the solutions of LMI's and Riccati equations. Finally, we derive a complete factorization theory of all-pass functions. Our results are obtained in the most general setting, without introducing any ad hoc assumption and can be applied to a variety of problems such as the discrete-time counterpart of the H
^∞
model reduction problems solved by Glover in continuous-time.