Identification of Dominant Subspaces for Linear Structured Parametric Systems and Model Reduction

TL;DR

This paper introduces a new model reduction method for structured linear parametric systems that identifies dominant subspaces, improving efficiency and applicability to large-scale systems.

Contribution

It connects interpolation-based reduction with system subspaces and proposes an algorithm that effectively reduces large-scale structured systems.

Findings

The method accurately identifies dominant subspaces.

It is computationally efficient for large-scale systems.

Numerical examples demonstrate its effectiveness.

Abstract

In this paper, we discuss a novel model reduction framework for generalized linear systems. The transfer functions of these systems are assumed to have a special structure, e.g., coming from second-order linear systems and time-delay systems, and they may also have parameter dependencies. Firstly, we investigate the connection between classic interpolation-based model reduction methods with the reachability and observability subspaces of linear structured parametric systems. We show that if enough interpolation points are taken, the projection matrices of interpolation-based model reduction encode these subspaces. As a result, we are able to identify the dominant reachable and observable subspaces of the underlying system. Based on this, we propose a new model reduction algorithm combining these features leading to reduced-order systems. Furthermore, we pay special attention to computational aspects of the approach and discuss its applicability to a large-scale setting. We illustrate the efficiency of the proposed approach with several numerical large-scale benchmark examples.