[2408.14115] Port-Hamiltonian Realizations of Positive Real Descriptor Systems
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Mathematics > Optimization and Control

arXiv:2408.14115 (math)
[Submitted on 26 Aug 2024]

Title:Port-Hamiltonian Realizations of Positive Real Descriptor Systems

Authors:Delin Chu, Volker Mehrmann
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Abstract: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.
Subjects: Optimization and Control (math.OC); Numerical Analysis (math.NA)
MSC classes: 93B05, 93B40, 93B52, 65F35
Cite as: arXiv:2408.14115 [math.OC]
  (or arXiv:2408.14115v1 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2408.14115

Submission history

From: Volker Mehrmann [view email]
[v1] Mon, 26 Aug 2024 09:01:37 UTC (20 KB)
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