Balanced Truncation of Networked Linear Passive Systems

TL;DR

This paper presents a balanced truncation method for reducing the complexity of networked linear passive systems, preserving passivity and synchronization, and providing error bounds, demonstrated through an example.

Contribution

It introduces a novel balanced truncation approach tailored for networked passive systems that maintains passivity and synchronization, with provable error bounds.

Findings

Reduced-order models preserve passivity and synchronization.

The method allows computation of approximation error bounds.

Demonstrated feasibility through a practical example.

Abstract

This paper studies model order reduction of multi-agent systems consisting of identical linear passive subsystems, where the interconnection topology is characterized by an undirected weighted graph. Balanced truncation based on a pair of specifically selected generalized Gramians is implemented on the asymptotically stable part of the full-order network model, which leads to a reduced-order system preserving the passivity of each subsystem. Moreover, it is proven that there exists a coordinate transformation to convert the resulting reduced-order model to a state-space model of Laplacian dynamics. Thus, the proposed method simultaneously reduces the complexity of the network structure and individual agent dynamics, and it preserves the passivity of the subsystems and the synchronization of the network. Moreover, it allows for the a priori computation of a bound on the approximation error. Finally, the feasibility of the method is demonstrated by an example.