Model Reduction of Second-order Network Systems using Graph Clustering

A general framework is proposed for structure preserving model reduction of a second-order network system. The method is based on graph clustering, and a recursive algorithm is proposed to find an appropriate clustering. Behaviors of nodes are interpreted by transfer functions, and the similarities of the behaviors among the nodes are quantized by the norms of the differences of their transfer functions. Then, we aggregate those nodes with closer behaviors and the reduced-order system is then generated by the projection associated with the resulting clustering. This paper clarifies that the new system preserves the network structures, i.e., it can be again interpreted as a second-order system defined on a connected undirected graph but with less nodes. Furthermore, a derivation of the approximation error bound is presented, and the proposed results are illustrated by means of an example.