Nudelman interpolation, parametrizations of lossless functions and balanced realizations

TL;DR

This paper introduces a new parametrization method for discrete-time stable all-pass multivariable systems using Nudelman interpolation, enabling efficient optimization in system identification and control.

Contribution

It presents a recursive balanced realization construction and multiple local parametrizations with an effective encoding strategy for lossless functions.

Findings

The proposed parametrizations exhibit excellent numerical stability.

The encoding strategy is highly efficient for optimization tasks.

New atlases of local parametrizations are developed for system analysis.

Abstract

We investigate the parametrization issue for discrete-time stable all-pass multivariable systems by means of a Schur algorithm involving a Nudelman interpolation condition. A recursive construction of balanced realizations is associated with it, that possesses a very good numerical behavior. Several atlases of charts or families of local parametrizations are presented and for each atlas a chart selection strategy is proposed. The last one can be viewed as a nice mutual encoding property of lossless functions and turns out to be very efficient. These parametrizations allow for solving optimization problems within the fields of system identification and optimal control.