Cross-Gramian-Based Dominant Subspaces

TL;DR

This paper introduces a novel dominant subspace model reduction method using the cross Gramian for linear systems, providing an a-priori error indicator and demonstrating efficiency through numerical examples.

Contribution

It extends the dominant subspace approach by leveraging the cross Gramian, offering a new computational technique and error estimation for linear system reduction.

Findings

The method effectively computes dominant subspaces using the cross Gramian.

An a-priori error indicator for the reduction method is proposed.

Numerical examples validate the efficiency and accuracy of the approach.

Abstract

A standard approach for model reduction of linear input-output systems is balanced truncation, which is based on the controllability and observability properties of the underlying system. The related dominant subspace projection model reduction method similarly utilizes these system properties, yet instead of balancing, the associated subspaces are directly conjoined. In this work we extend the dominant subspace approach by computation via the cross Gramian for linear systems, and describe an a-priori error indicator for this method. Furthermore, efficient computation is discussed alongside numerical examples illustrating these findings.