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

TL;DR

This paper provides a comprehensive state-space characterization of discrete-time all-pass rational matrix functions, facilitating model reduction, factorization, and analysis of related LMIs and Riccati equations in a general setting.

Contribution

It introduces a general, assumption-free characterization of discrete-time all-pass functions from state-space models, extending continuous-time theory to discrete systems.

Findings

General state-space characterization of all-pass functions

Application to model reduction and factorization

Useful insights into LMIs and Riccati equations

Abstract

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.