Identification of dominant subspaces for model reduction of structured parametric systems

Abstract

SummaryIn this paper, we discuss a novel model reduction framework for linear structured dynamical systems. The transfer functions of these systems are assumed to have a special structure, for example, coming from second‐order linear systems or 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. Consequently, 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 and leading to reduced‐order systems. Furthermore, we discuss computational aspects of the approach and its applicability to a large‐scale setting. We illustrate the efficiency of the proposed approach with several numerical large‐scale benchmark examples.