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PreprintarXiv licencearXiv

Exponential stability of port-Hamiltonian systems with unstructured, measurable Hamiltonian densities

  • Heinrich Kuettler
  • Marcus Waurick
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Abstract

For first-order port-Hamiltonian systems in the dissipative setting considered here, we characterise exponential stability without any further regularity or block-structure assumption on the Hamiltonian density, thus closing a gap persisting in the literature. The proof requires revisiting the computation of the adjoint generator of the port-Hamiltonian semigroup. Finally, we provide both examples and non-examples showcasing the inconclusiveness of known conditions on the Hamiltonian densities necessary for the application of characterisation results in the literature.

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Cite

BibTeXRIS
BibTeX
@misc{kuettler2026exponential,
  title = {{Exponential stability of port-Hamiltonian systems with unstructured, measurable Hamiltonian densities}},
  author = {Heinrich Kuettler and Marcus Waurick},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.41326},
  eprint = {2610.41326},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.41326},
}
RIS
TY  - UNPB
TI  - Exponential stability of port-Hamiltonian systems with unstructured, measurable Hamiltonian densities
AU  - Heinrich Kuettler
AU  - Marcus Waurick
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2610.41326
UR  - https://arxiv.org/abs/2610.41326
AB  - For first-order port-Hamiltonian systems in the dissipative setting considered here, we characterise exponential stability without any further regularity or block-structure assumption on the Hamiltonian density, thus closing a gap persisting in the literature. The proof requires revisiting the computation of the adjoint generator of the port-Hamiltonian semigroup. Finally, we provide both examples and non-examples showcasing the inconclusiveness of known conditions on the Hamiltonian densities necessary for the application of characterisation results in the literature.
ER  -