Interconnection of port-Hamiltonian systems is not dynamical
Abstract
The interconnection of port-Hamiltonian systems is usually understood as structure-preserving due to the geometric fact that the composition of the underlying Dirac structures produces again a Dirac structure. Pointwise, this is doubtless true, but when comparing dynamical systems, their trajectories are usually compared, and trajectories usually obey some regularity assumptions. It is shown that both classical and weak solutions do not necessarily exhibit a one-to-one correspondence between solutions of the interconnected port-Hamiltonian system, and the dynamical system realising the interconnection. In the mostly studied cases of constant Dirac structures or port-Hamiltonian ODE systems, both systems are behaviourally equivalent; for non-constant Dirac structures, a sufficient condition is given.
Related
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- Stable Dynamical Mass Transportation via port-Hamiltonian Structure
- Exponential stability of port-Hamiltonian systems with unstructured, measurable Hamiltonian densities
- Input-to-state stability of second-order port-Hamiltonian systems under nonlinear dynamic boundary feedback
- A class of port-Hamiltonian systems with general time delays
BibTeX
@misc{kirchhoff2026interconnection,
title = {{Interconnection of port-Hamiltonian systems is not dynamical}},
author = {Jonas Kirchhoff},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29731},
eprint = {2608.29731},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29731},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Interconnection of port-Hamiltonian systems is not dynamical
AU - Jonas Kirchhoff
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.29731
UR - https://arxiv.org/abs/2608.29731
AB - The interconnection of port-Hamiltonian systems is usually understood as structure-preserving due to the geometric fact that the composition of the underlying Dirac structures produces again a Dirac structure. Pointwise, this is doubtless true, but when comparing dynamical systems, their trajectories are usually compared, and trajectories usually obey some regularity assumptions. It is shown that both classical and weak solutions do not necessarily exhibit a one-to-one correspondence between solutions of the interconnected port-Hamiltonian system, and the dynamical system realising the interconnection. In the mostly studied cases of constant Dirac structures or port-Hamiltonian ODE systems, both systems are behaviourally equivalent; for non-constant Dirac structures, a sufficient condition is given.
ER -