Model Reduction in the Loewner Framework for Second-Order Network Systems on Graphs

This paper studies the model reduction problem in the Loewner framework for second-order network systems evolving on graphs. The selection of particular sets of tangential interpolation data allows constructing reduced order models which interpolate the underlying network system while preserving the second-order structure of the system. The conditions that the tangential interpolation data must satisfy are established on the basis of the block structure of the Loewner matrices. We use this result to link the Loewner matrices to the cluster matrix gained by partitioning the graph associated with the underlying model. Finally, we provide an illustrative example to validate the obtained results.