Model Reduction for Systems with Inhomogeneous Initial Conditions

TL;DR

This paper introduces a novel model reduction method for linear systems with inhomogeneous initial conditions, decomposing responses into components and reducing them independently for improved approximation.

Contribution

It proposes a new approach that separately reduces the response components for systems with initial conditions and combines them, enhancing flexibility and accuracy.

Findings

Better approximation properties than existing methods

Flexible reduction of response components

Applicable to linear time-invariant systems

Abstract

We consider the model reduction problem for linear time-invariant dynamical systems having nonzero (but otherwise indeterminate) initial conditions. Building upon the observation that the full system response is decomposable as a superposition of the response map for an unforced system having nontrivial initial conditions and the response map for a forced system having null initial conditions, we develop a new approach that involves reducing these component responses independently and then combining the reduced responses into an aggregate reduced system response. This approach allows greater flexibility and offers better approximation properties than other comparable methods.