Structure-Preserving Interpolation for Model Reduction of Parametric Bilinear Systems

TL;DR

This paper develops a framework for reducing complex parametric bilinear systems while preserving their inherent structure and parameter dependencies, ensuring accurate and efficient simplified models.

Contribution

It introduces a general interpolation-based approach for structure-preserving model reduction applicable to various parametric bilinear systems.

Findings

The method maintains system structure and parameter dependencies in reduced models.

The framework is validated on two benchmark examples with different parameter dependencies.

The approach ensures accurate transfer function interpolation for reduced-order models.

Abstract

In this paper, we present an interpolation framework for structure-preserving model order reduction of parametric bilinear dynamical systems. We introduce a general setting, covering a broad variety of different structures for parametric bilinear systems, and then provide conditions on projection spaces for the interpolation of structured subsystem transfer functions such that the system structure and parameter dependencies are preserved in the reduced-order model. Two benchmark examples with different parameter dependencies are used to demonstrate the theoretical analysis.