Port-Hamiltonian Realizations of Positive Real Descriptor Systems
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916369775198208 |
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| author | Chu, Delin Mehrmann, Volker |
| author_facet | Chu, Delin Mehrmann, Volker |
| contents | The relationship between port-Hamiltonian and positive real descriptor systems is investigated. It is well-known that port-Hamiltonian systems are positive real, but the converse implication does not always hold. In [K. Cherifi, H. Gernandt, and D. Hinsen. The difference between port-Hamiltonian, passive and positive real descriptor systems. Math. Control Signals Systems, pages 1-32, 2023] sufficient conditions for the converse are presented. We refine these conditions and present for a completely controllable, completely observable and positive real descriptor system a necessary and sufficient condition as well as an explicit method to compute a port-Hamiltonian realization of a general positive real descriptor system. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_14115 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Port-Hamiltonian Realizations of Positive Real Descriptor Systems Chu, Delin Mehrmann, Volker Optimization and Control Numerical Analysis 93B05, 93B40, 93B52, 65F35 The relationship between port-Hamiltonian and positive real descriptor systems is investigated. It is well-known that port-Hamiltonian systems are positive real, but the converse implication does not always hold. In [K. Cherifi, H. Gernandt, and D. Hinsen. The difference between port-Hamiltonian, passive and positive real descriptor systems. Math. Control Signals Systems, pages 1-32, 2023] sufficient conditions for the converse are presented. We refine these conditions and present for a completely controllable, completely observable and positive real descriptor system a necessary and sufficient condition as well as an explicit method to compute a port-Hamiltonian realization of a general positive real descriptor system. |
| title | Port-Hamiltonian Realizations of Positive Real Descriptor Systems |
| topic | Optimization and Control Numerical Analysis 93B05, 93B40, 93B52, 65F35 |
| url | https://arxiv.org/abs/2408.14115 |