Relationship between dissipativity concepts for linear time-varying port-Hamiltonian systems
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913622641344512 |
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| author | Cherifi, Karim Gernandt, Hannes Hinsen, Dorothea Mehrmann, Volker Morandin, Riccardo |
| author_facet | Cherifi, Karim Gernandt, Hannes Hinsen, Dorothea Mehrmann, Volker Morandin, Riccardo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16396 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Relationship between dissipativity concepts for linear time-varying port-Hamiltonian systems Cherifi, Karim Gernandt, Hannes Hinsen, Dorothea Mehrmann, Volker Morandin, Riccardo Optimization and Control 93A30, 65L80, 93B17, 93B11 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. |
| title | Relationship between dissipativity concepts for linear time-varying port-Hamiltonian systems |
| topic | Optimization and Control 93A30, 65L80, 93B17, 93B11 |
| url | https://arxiv.org/abs/2412.16396 |