Model reduction for linear systems with low-rank switching

TL;DR

This paper presents a new model reduction technique for large-scale linear switched systems with low-rank switching, using an envelope system approach to enable standard reduction methods and preserve stability.

Contribution

It introduces the envelope system concept for reducing low-rank switched systems and provides stability preservation and error bounds.

Findings

Effective reduction of large-scale LSS demonstrated

Preserves quadratic Lyapunov stability in reduced models

Numerical examples confirm method efficacy

Abstract

We introduce a novel model order reduction method for large-scale linear switched systems (LSS) where the coefficient matrices are affected by a low-rank switching. The key idea is to replace the LSS by a non-switched system with extended input and output vectors - called the envelope system - which is able to reproduce the dynamical behavior of the original LSS by applying a certain feedback law. The envelope system can be reduced using standard model order reduction schemes and then transformed back to an LSS. Furthermore, we present an upper bound for the output error of the reduced-order LSS and show how to preserve quadratic Lyapunov stability. The approach is tested by means of various numerical examples demonstrating the efficacy of the presented method.