Structure-preserving discretization for port-Hamiltonian descriptor systems

Authors

Abstract

We extend the modeling framework of port-Hamiltonian descriptor systems to include under- and overdetermined systems and arbitrary differentiable Hamiltonian functions. This structure is associated with a Dirac structure that encloses its energy balance properties. In particular, port-Hamiltonian systems are naturally passive and Lyapunov stable, because the Hamiltonian defines a Lyapunov function. The explicit representation of input and dissipation in the structure make these systems particularly suitable for output feedback control. It is shown that this structure is invariant under a wide class of nonlinear transformations, and that it can be naturally modularized, making it adequate for automated modeling. We investigate then the application of time-discretization schemes to these systems and we show that, under certain assumptions on the Hamiltonian, structure preservation is achieved for some methods. Relevant examples are provided.

Citation

Journal: 2019 IEEE 58th Conference on Decision and Control (CDC)
Year: 2019
Volume:
Issue:
Pages: 6863–6868
Publisher: IEEE
DOI: 10.1109/cdc40024.2019.9030180

BibTeX

@inproceedings{Mehrmann_2019,
  title={{Structure-preserving discretization for port-Hamiltonian descriptor systems}},
  DOI={10.1109/cdc40024.2019.9030180},
  booktitle={{2019 IEEE 58th Conference on Decision and Control (CDC)}},
  publisher={IEEE},
  author={Mehrmann, Volker and Morandin, Riccardo},
  year={2019},
  pages={6863--6868}
}

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References

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