Limit Cycles in Locally Hamiltonian Systems with Dissipation

Authors

Abstract

We consider systems that possess a local but non-global port-Hamiltonian representation. We show that non-globality is a consequence of the phase-space topology and that local port-Hamiltonian systems may transgress the dissipation inequality satisfied by their global counterparts. Far from being a defect, non-globality extends the modeling power of port-Hamiltonian systems by providing a framework to model cyclic physical processes for energy conversion and extraction.

Keywords

Port-Hamiltonian systems; passivity; symplectic systems; locally Hamiltonian systems; discontinuous Hamiltonian; limit cycles

Citation

Journal: IFAC-PapersOnLine
Year: 2021
Volume: 54
Issue: 19
Pages: 192–197
Publisher: Elsevier BV
DOI: 10.1016/j.ifacol.2021.11.077
Note: 7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2021- Berlin, Germany, 11-13 October 2021

BibTeX

@article{Casta_os_2021,
  title={{Limit Cycles in Locally Hamiltonian Systems with Dissipation}},
  volume={54},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2021.11.077},
  number={19},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Castaños, Fernando and Gromov, Dmitry},
  year={2021},
  pages={192--197}
}

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