Model Reduction by Moment Matching for Linear Coupled Systems

This paper focuses on model order reduction of coupled systems using a moment matching approach to preserve the internal structure and coupling of the system. By defining moments in the time domain, we propose a moment matching method that solves Sylvester equations associated with the subsystems’ moments to obtain the reduction matrix. The resulting reduced-order model is parameterized with a free parameter, allowing for the enforcement of additional properties such as pole preservation and pole placement. We demonstrate the effectiveness of the proposed method through an illustrative example.

I. Introduction

Coupled systems consisting of multiple subsystems are described by ordinary differential equations (ODEs), partial differential equations (PDEs), and differential algebraic equations (DAEs) [1]. These systems appear in many engineering fields and can simulate various complex physical phenomena. In these coupled systems, different subsystems have numerous initial variables that interact with each other, resulting in high-dimensional coupled systems.