Identification of Dominant Subspaces for Linear Structured Parametric Systems and Model Reduction
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.
Cite
@article{arxiv.1910.13945,
title = {Identification of Dominant Subspaces for Linear Structured Parametric Systems and Model Reduction},
author = {Peter Benner and Pawan Goyal and Igor Pontes Duff},
journal= {arXiv preprint arXiv:1910.13945},
year = {2019}
}