Stability-Preserving Model Reduction of Networked Lur'e Systems

TL;DR

This paper introduces a graph clustering-based model reduction method for Lur'e network systems that preserves stability and provides bounds on approximation error, demonstrated through numerical examples.

Contribution

It presents a novel stability-preserving model reduction technique for Lur'e networks using graph clustering, with error bounds.

Findings

Reduced models maintain network structure and stability

Upper bounds on input-output error are derived

Numerical examples validate the approach

Abstract

This paper proposes a model reduction approach for simplifying the interconnection topology of Lur'e network systems. A class of reduced-order models are generated by the projection framework based on graph clustering, which not only preserve the network structure but also ensure absolute stability. Furthermore, we provide an upper bound on the input-output approximation error between the original and reduced-order Lur'e network systems, which is expressed as a function of the characteristic matrix of graph clustering. Finally, the results are illustrated via a numerical example.