Energy-stable Port-Hamiltonian Systems

TL;DR

This paper introduces energy-stable port-Hamiltonian (espH) systems, combining energy stability with port-Hamiltonian structure to ensure structure preservation during discretization and model reduction.

Contribution

It extends energy-stable systems with input-output ports to create a new espH formulation that maintains its structure throughout numerical methods.

Findings

espH systems preserve energy stability during discretization

The formulation maintains structure during model reduction

The approach facilitates stable and structure-preserving simulations

Abstract

We combine energy-stable and port-Hamiltonian (pH) systems to obtain energy-stable port-Hamiltonian (espH) systems. The idea is to extend the known energy-stable systems with an input-output port, which results in a pH formulation. One advantage of the new espH formulation is that it naturally preserves its espH structure throughout discretization (in space and time) and model reduction.