Hybrid port–Hamiltonian systems: From parameterized incidence matrices to hybrid automata

Authors

Abstract

This paper shows how to formally design a hybrid automaton model for a wide class of dissipative physical systems with sources and switching topology. This method is based on a mathematical representation of the dynamic network graph and of its dual graph, using the hybrid incidence matrix, and on a constructive method for analyzing admissible and constrained configurations. The port–Hamiltonian representation associated with the set of hybrid system configurations, parameterized by the discrete state of the switches, is synthesized to be part of the hybrid automaton of the system. This is a further step towards a generic control synthesis for physical switching systems.

Keywords

Hybrid dynamical systems; Modeling; Hybrid automata; Dynamic network graph; Incidence matrix; Analysis; Admissible configurations; Constrained configurations

Citation

Journal: Nonlinear Analysis: Theory, Methods & Applications
Year: 2006
Volume: 65
Issue: 6
Pages: 1106–1122
Publisher: Elsevier BV
DOI: 10.1016/j.na.2005.12.013
Note: Hybrid Systems and Applications (5)

BibTeX

@article{Valentin_2006,
  title={{Hybrid port–Hamiltonian systems: From parameterized incidence matrices to hybrid automata}},
  volume={65},
  ISSN={0362-546X},
  DOI={10.1016/j.na.2005.12.013},
  number={6},
  journal={Nonlinear Analysis: Theory, Methods &amp; Applications},
  publisher={Elsevier BV},
  author={Valentin, C. and Magos, M. and Maschke, B.},
  year={2006},
  pages={1106--1122}
}

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References

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