Balancing-based model reduction for switched descriptor systems

TL;DR

This paper introduces a new certified model order reduction algorithm for large-scale switched descriptor systems, extending balanced truncation techniques and providing detailed error analysis including numerical approximation errors.

Contribution

It presents the first large-scale applicable MOR method for switched descriptor systems, combining reformulation and balanced truncation with a comprehensive error analysis.

Findings

The method is applicable to large-scale systems.

The standard error bound is insufficient without accounting for numerical errors.

Numerical experiments validate the theoretical error bounds.

Abstract

We present a novel certified model order reduction (MOR) algorithm for switched descriptor systems applicable to large-scale systems. Our algorithm combines the idea of [Hossain \& Trenn, Technical report, 2023] to reformulate the switched descriptor system as a switched ordinary differential equation with jumps and an extension of the balanced truncation for switched ODE from [Pontes Duff et al., IEEE Trans.~Automat.~Control, 2020]. Besides being the first MOR method for switched descriptor systems applicable to the large-scale setting, we give a detailed numerical analysis by incorporating the error in the computation of the system Gramians in the a-priori error bound for the output of the reduced system. In more detail, we demonstrate, theoretically and numerically, that the standard error bound is not applicable, and a certificate must account for the numerical approximation errors.