Graph structure-preserving model reduction of linear network systems

摘要

In this paper, a structure-preserving model reduction procedure is developed for linear network systems. The system is evolving on a graph which is assumed to be connected, weighted and undirected. A projection matrix, called cluster matrix is used to obtain the reduced-order model. In the approach, vertices in the graph having similar frequency responses are aggregated, i.e. the number of vertices is reduced. It is shown that reduced order models are still network systems with connected, weighted and undirected graphs. Moreover, we give an exact error between the original and reduced order models, which is bounded. Finally, an example demonstrates the proposed results.