Two energy methods for distributed port-Hamiltonian systems and their application to stability analysis
Optimization and Control
2025-12-01 v1 Analysis of PDEs
Functional Analysis
Abstract
We develop two local energy methods for distributed parameter port-Hamiltonian (pH) systems on one-dimensional spatial domains. The methods are applied to derive a characterization of exponential stability directly in terms of the energy passing through the boundary over a given time horizon. The resulting condition is verified for a network of vibrating strings where existing sufficient conditions cannot be applied. Moreover, we use a local energy method to study the short-time behavior of pH systems with boundary damping which was recently studied in the context of hypocoercivity.
Cite
@article{arxiv.2511.23336,
title = {Two energy methods for distributed port-Hamiltonian systems and their application to stability analysis},
author = {Marco Roschkowski and Hannes Gernandt},
journal= {arXiv preprint arXiv:2511.23336},
year = {2025}
}