Beyond Singular Perturbation for linear port-Hamiltonian systems

Abstract

This paper is concerned with the structure/passivity-preserving model order reduction of linear port-Hamiltonian systems. We first present, with the help of the implicit port-Hamiltonian formulation, some issues related to the standard Singular Perturbation technique. We use a simple example to analyze these aspects, paving the way for a recent approach developed to reduce the model order, called Beyond Singular Perturbation. This technique leverages the description of the dominant evolution of the original system whenever a time-scale separation is present among its dynamics. With this tool, we study the system’s Hamiltonian time evolution, showing that we can successfully reconstruct the dominant behavior of the Hamiltonian by slightly modifying the storage function of the resulting reduced-order model. We conclude the work with a discussion about the class of input signals that allow a good performance of the reduced-order model.