Authors

Birgit Jacob, Kirsten A. Morris, Hans Zwart

Abstract

The zero dynamics of infinite-dimensional systems can be difficult to characterize. The zero dynamics of boundary control systems are particularly problematic. In this paper the zero dynamics of port-Hamiltonian systems are studied. A complete characterization of the zero dynamics for port-Hamiltonian systems with invertible feedthrough as another port-Hamiltonian system on the same state space is given. It is shown that the zero dynamics for any port-Hamiltonian system with commensurate wave speeds are a well-posed system, and are also a port-Hamiltonian system. Examples include wave equations with uniform wave speed on a network. A constructive procedure for calculation of the zero dynamics that can be used for very large system order is provided.

Keywords

Port-Hamiltonian system; Distributed parameter systems; Boundary control; Zero dynamics; Networks; Coupled wave equations

Citation

BibTeX

@article{Jacob_2019,
  title={{Zero dynamics for networks of waves}},
  volume={103},
  ISSN={0005-1098},
  DOI={10.1016/j.automatica.2019.02.010},
  journal={Automatica},
  publisher={Elsevier BV},
  author={Jacob, Birgit and Morris, Kirsten A. and Zwart, Hans},
  year={2019},
  pages={310--321}
}

Download the bib file

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