Structure-preserving coupling and decoupling of port-Hamiltonian systems

Authors

Matthias Ehrhardt, Michael Günther, Daniel Ševčovič

Abstract

The port-Hamiltonian framework is a structure-preserving modeling approach that preserves key physical properties such as energy conservation and dissipation. When subsystems are modeled as port-Hamiltonian systems (pHS) with linearly related inputs and outputs, their interconnection remains port-Hamiltonian. This paper introduces a systematic method for transforming coupled port Hamiltonian ordinary differential equations systems (pHODE) into a single monolithic formulation, and for decomposing a monolithic system into weakly coupled subsystems. The monolithic representation ensures stability and structural integrity, whereas the decoupled form enables efficient distributed simulation via operator splitting or dynamic iteration.

Keywords

coupling and decoupling, ordinary differential equations, port-hamiltonian systems, structure preservation

Citation

• Journal: Applied Mathematics Letters
• Year: 2026
• Volume: 177
• Issue:
• Pages: 109894
• Publisher: Elsevier BV
• DOI: 10.1016/j.aml.2026.109894

BibTeX

@article{Ehrhardt_2026,
  title={{Structure-preserving coupling and decoupling of port-Hamiltonian systems}},
  volume={177},
  ISSN={0893-9659},
  DOI={10.1016/j.aml.2026.109894},
  journal={Applied Mathematics Letters},
  publisher={Elsevier BV},
  author={Ehrhardt, Matthias and Günther, Michael and Ševčovič, Daniel},
  year={2026},
  pages={109894}
}

Download the bib file

References

• Buchfink P, Glas S, Zwart H (2026) Energy-stable port-Hamiltonian systems. Applied Mathematics Letters 173:109784. https://doi.org/10.1016/j.aml.2025.10978 – 10.1016/j.aml.2025.109784
• Cervera J, van der Schaft AJ, Baños A (2007) Interconnection of port-Hamiltonian systems and composition of Dirac structures. Automatica 43(2):212–225. https://doi.org/10.1016/j.automatica.2006.08.01 – 10.1016/j.automatica.2006.08.014
• Jäschke J, Ehrhardt M, Günther M, Jacob B (2022) A port-Hamiltonian formulation of coupled heat transfer. Mathematical and Computer Modelling of Dynamical Systems 28(1):78–94. https://doi.org/10.1080/13873954.2022.203863 – 10.1080/13873954.2022.2038637
• Jäschke J, Ehrhardt M, Günther M, Jacob B (2022) A Two-Dimensional port-Hamiltonian Model for Coupled Heat Transfer. Mathematics 10(24):4635. https://doi.org/10.3390/math1024463 – 10.3390/math10244635
• Jacob, (2012)
• Bartel A, Günther M, Jacob B, Reis T (2023) Operator splitting based dynamic iteration for linear differential-algebraic port-Hamiltonian systems. Numer Math 155(1–2):1–34. https://doi.org/10.1007/s00211-023-01369- – 10.1007/s00211-023-01369-5
• Mehrmann V, Morandin R (2019) Structure-preserving discretization for port-Hamiltonian descriptor systems. 2019 IEEE 58th Conference on Decision and Control (CDC) 6863–686 – 10.1109/cdc40024.2019.9030180
• Altmann R, Mehrmann V, Unger B (2021) Port-Hamiltonian formulations of poroelastic network models. Mathematical and Computer Modelling of Dynamical Systems 27(1):429–452. https://doi.org/10.1080/13873954.2021.197513 – 10.1080/13873954.2021.1975137
• Bartel A, Diab M, Frommer A, Günther M, Marheineke N (2025) Splitting techniques for DAEs with port-Hamiltonian applications. Applied Numerical Mathematics 214:28–53. https://doi.org/10.1016/j.apnum.2025.03.00 – 10.1016/j.apnum.2025.03.004
• Lorenz J, Zwerschke T, Günther M, Schäfers K (2025) Operator splitting for coupled linear port-Hamiltonian systems. Applied Mathematics Letters 160:109309. https://doi.org/10.1016/j.aml.2024.10930 – 10.1016/j.aml.2024.109309
• Günther, Port-Hamiltonian Systems: A useful approach in electrical engineering?. (2022)
• Günther M, Bartel A, Jacob B, Reis T (2020) Dynamic iteration schemes and port‐Hamiltonian formulation in coupled differential‐algebraic equation circuit simulation. Circuit Theory & Apps 49(2):430–452. https://doi.org/10.1002/cta.287 – 10.1002/cta.2870
• Di Persio, (2025)