On model reduction by least squares moment matching

TL;DR

This paper introduces a new time-domain characterization of least squares moment matching for model reduction in linear systems, providing a parameterized family of reduced models with improved approximation.

Contribution

It offers a novel time-domain perspective on least squares moment matching, enabling the derivation of a parameterized family of reduced models.

Findings

New time-domain characterization of least squares moment matching

Parameterized family of reduced models achieved

Numerical example demonstrating effectiveness

Abstract

The paper addresses the model reduction problem by least squares moment matching for continuous-time, linear, time-invariant systems. The basic idea behind least squares moment matching is to approximate a transfer function by ensuring that the interpolation conditions imposed by moment matching are satisfied in a least squares sense. This idea is revisited using invariance equations and steady-state responses to provide a new time-domain characterization of least squares moment matching. The characterization, in turn, is then used to obtain a parameterized family of models achieving least squares moment matching. The theory is illustrated by a worked-out numerical example.