Skip to content
DraconiticResearch
Search Sources API
182,469 studies31 sourcesUpdated 23 min ago
PreprintCC BY 4.0arXiv

On the Stability Analysis of Infinite-Dimensional Port-Hamiltonian Systems Within the Variational Framework

  • Moritz Leitner
  • Lukas Ecker
  • Markus Schöberl
Open at sourcePDFDOICite

Abstract

This paper addresses the stability analysis of a class of linear infinite-dimensional port-Hamiltonian systems formulated within the variational framework. We derive verifiable conditions for the equivalence of the Hamiltonian-induced energy norm and the natural state-space norm, as well as for the generation of a contraction semigroup by the associated system operator. The semigroup generation result is obtained by establishing dissipativity and verifying the required range condition. The proposed conditions simplify the functional-analytic stability analysis of this class of systems in a manner similar to established results for the Stokes-Dirac setting.

Related

  1. Well-Posedness and Strong Convergence of Infinite-Dimensional Port-Hamiltonian Primal-Dual Gradient Dynamics
    O. V. Iftime, A. J. van der Schaft
    arXivPreprintarXiv licenceFull textOptimisation & controlarXiv
  2. BIBO stability in infinite dimensions: extensions and limitations of finite-dimensional theory
    Sahiba Arora, Alexander A. Wierzba
    arXivPreprintarXiv licenceFull textAnalysis & PDEsOptimisation & controlarXiv
  3. Sampling with Autoregressive Clock Jitter: Infinite-Dimensional Stability Failure and Finite-Dimensional Conditioning
    Daniele Gerosa, Thomas Eriksson
    arXivPreprintCC BY-NC-ND 4.0Full textGeneral mathematicsarXiv
  4. A unified variational framework for augmented Lagrangian preconditioning of saddle point systems: applications to mixed-dimensional and fictitious domain methods
    Michele Benzi, Marco Feder, Luca Heltai +1
    arXivPreprintCC BY 4.0Full textNumerical analysis & scientific computingarXiv
  5. A Pricing and Hedging Framework for Infinite-Dimensional Financial Markets
    Hanchao Liu
    arXivPreprintarXiv licenceFull textAnalysis & PDEsProbabilityarXiv

Cite

BibTeXRIS
BibTeX
@misc{leitner2026stability,
  title = {{On the Stability Analysis of Infinite-Dimensional Port-Hamiltonian Systems Within the Variational Framework}},
  author = {Moritz Leitner and Lukas Ecker and Markus Schöberl},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.39724},
  eprint = {2610.39724},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.39724},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On the Stability Analysis of Infinite-Dimensional Port-Hamiltonian Systems Within the Variational Framework
AU  - Moritz Leitner
AU  - Lukas Ecker
AU  - Markus Schöberl
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.39724
UR  - https://arxiv.org/abs/2610.39724
AB  - This paper addresses the stability analysis of a class of linear infinite-dimensional port-Hamiltonian systems formulated within the variational framework. We derive verifiable conditions for the equivalence of the Hamiltonian-induced energy norm and the natural state-space norm, as well as for the generation of a contraction semigroup by the associated system operator. The semigroup generation result is obtained by establishing dissipativity and verifying the required range condition. The proposed conditions simplify the functional-analytic stability analysis of this class of systems in a manner similar to established results for the Stokes-Dirac setting.
ER  -