# Reduction of Second-Order Network Systems with Structure Preservation

arXiv: https://arxiv.org/abs/1706.01751 · HTML: https://mlsanity.com/paper/1706.01751/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jun 2017.

## Built on by (most cited first, 1 of 1)

- [Controllability of Coarsely Measured Networked Linear Dynamical Systems (Extended Version)](https://mlsanity.com/paper/2206.10569/) (2022)

## Abstract (arXiv)

This paper proposes a general framework for structure-preserving model reduction of a secondorder network system based on graph clustering. In this approach, vertex dynamics are captured by the transfer functions from inputs to individual states, and the dissimilarities of vertices are quantified by the H2-norms of the transfer function discrepancies. A greedy hierarchical clustering algorithm is proposed to place those vertices with similar dynamics into same clusters. Then, the reduced-order model is generated by the Petrov-Galerkin method, where the projection is formed by the characteristic matrix of the resulting network clustering. It is shown that the simplified system preserves an interconnection structure, i.e., it can be again interpreted as a second-order system evolving over a reduced graph. Furthermore, this paper generalizes the definition of network controllability Gramian to second-order network systems. Based on it, we develop an efficient method to compute H2-norms and derive the approximation error between the full-order and reduced-order models. Finally, the approach is illustrated by the example of a small-world network.