A Connection Between Time Domain Model Order Reduction and Moment Matching for LTI Systems

TL;DR

This paper establishes a theoretical connection between time domain model order reduction using orthogonal polynomials and moment matching in LTI systems, revealing limitations and similarities of these approaches.

Contribution

It extends previous MOR methods by linking them to rational Krylov subspaces and moment matching, providing new insights into their theoretical relationship.

Findings

Time domain MOR can be as accurate as moment matching under certain conditions.

A Sylvester equation is identified as a key link between the methods.

Numerical examples illustrate the theoretical connection.

Abstract

We investigate the time domain model order reduction (MOR) framework using general orthogonal polynomials by Jiang and Chen 2012 and extend their idea by exploiting the structure of the corresponding linear system of equations. Identifying an equivalent Sylvester equation, we show a connection to a rational Krylov subspace, and thus to moment matching. This theoretical link between the MOR techniques is illustrated by three numerical examples. For linear time-invariant systems, the link also motivates that the time domain approach can be at best as accurate as moment matching, since the expansion points are fixed by the choice of the polynomial basis, while in moment matching they can be adapted to the system.