Port-Hamiltonian realizations of non-minimal linear time-invariant systems

Authors

Christopher Beattie, Volker Mehrmann, Hongguo Xu

Abstract

Numerical methods for developing port-Hamiltonian representations of general linear time-invariant systems are studied. The approach extends previous port-Hamiltonian characterizations to include the general non-minimal case and the case where the feedthrough term fails to have an invertible symmetric part. The resulting construction is able to identify infeasibility when the system fails to be port-Hamiltonian, and allows for the incorporation of perturbations in order to arrive at a nearby port-Hamiltonian system. Results are illustrated via numerical examples.

Keywords

93a30, 93b11, 93b17, even pencil, kalman-yakubovich-popov inequality, lyapunov inequality, passivity, port-hamiltonian system, quadratic eigenvalue problem, stability, system transformation

Citation

• Journal: Mathematics of Control, Signals, and Systems
• Year: 2026
• Volume:
• Issue:
• Pages:
• Publisher: Springer Science and Business Media LLC
• DOI: 10.1007/s00498-025-00432-w

BibTeX

@article{Beattie_2026,
  title={{Port-Hamiltonian realizations of non-minimal linear time-invariant systems}},
  ISSN={1435-568X},
  DOI={10.1007/s00498-025-00432-w},
  journal={Mathematics of Control, Signals, and Systems},
  publisher={Springer Science and Business Media LLC},
  author={Beattie, Christopher and Mehrmann, Volker and Xu, Hongguo},
  year={2026}
}

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