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arXiv · 2412.16396

Relationship between dissipativity concepts for linear time-varying port-Hamiltonian systems

Karim Cherifi·Hannes Gernandt·Dorothea Hinsen·Volker Mehrmann·Riccardo Morandin
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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.

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Karim Cherifi, Hannes Gernandt, Dorothea Hinsen, Volker Mehrmann, Riccardo Morandin. 2024-12-20. Relationship between dissipativity concepts for linear time-varying port-Hamiltonian systems. https://arxiv.org/abs/2412.16396

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