Relationship between dissipativity concepts for linear time-varying port-Hamiltonian systems
Abstract The relationship between different dissipativity concepts for linear time-varying systems is studied, in particular between port-Hamiltonian systems, passive systems, and systems with nonnegative supply. It is shown that linear time-varying port-Hamiltonian systems are passive, have nonnegative supply rates, and solve (under different smoothness assumptions) Kalman–Yakubovich–Popov differential and integral inequalities. The converse relations are also studied in detail. In particular, sufficient conditions are presented to obtain a port-Hamiltonian representation starting from any of the other dissipativity concepts. Two applications are presented.
Authors
- Volker Mehrmann (ORCID: https://orcid.org/0000-0001-5051-2870)
- Riccardo Morandin (ORCID: https://orcid.org/0000-0003-2511-041X)
- Hannes Gernandt (ORCID: https://orcid.org/0000-0001-7364-4606)
- Karim Cherifi (ORCID: https://orcid.org/0000-0003-1294-9291)
- Dorothea Hinsen (ORCID: https://orcid.org/0000-0002-6576-9430)
Institutions
- University of Wuppertal (DE)
- Wuppertal Institute for Climate, Environment and Energy (DE)
- Fraunhofer Research Institution for Energy Infrastructures and Geotechnologies IEG (DE)
- Technische Universität Berlin (DE)
- Otto-von-Guericke-Universität Magdeburg (DE)
Publication Details
- Journal
- Mathematics of Control Signals and Systems
- Published
- 2025-07-20
- DOI
- https://doi.org/10.1007/s00498-025-00421-z
- Primary Topic
- Control and Stability of Dynamical Systems
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Deutsche Forschungsgemeinschaft
- Bundesministerium für Bildung und Forschung
- Otto von Guericke University Magdeburg