PreprintCC BY 4.0arXiv
Descriptor representations of geometric port-Hamiltonian systems on Hilbert spaces
Abstract
We establish conversions in both directions between geometric and descriptor representations of linear port-Hamiltonian systems on infinite-dimensional Hilbert spaces. For the geometric-to-descriptor conversion, we represent the possibly multivalued inverse Dirac relation by a skew-adjoint operator on enlarged Hilbert spaces, retaining the original operator-domain restrictions. The construction accommodates internal and external ports. We show that the conversions preserve trajectories and the power balance. An incompressible Kelvin--Voigt solid illustrates the results.
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BibTeX
@misc{fischer2026descriptor,
title = {{Descriptor representations of geometric port-Hamiltonian systems on Hilbert spaces}},
author = {Anna Fischer and Timo Reis},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06080},
eprint = {2611.06080},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06080},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Descriptor representations of geometric port-Hamiltonian systems on Hilbert spaces
AU - Anna Fischer
AU - Timo Reis
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06080
UR - https://arxiv.org/abs/2611.06080
AB - We establish conversions in both directions between geometric and descriptor representations of linear port-Hamiltonian systems on infinite-dimensional Hilbert spaces. For the geometric-to-descriptor conversion, we represent the possibly multivalued inverse Dirac relation by a skew-adjoint operator on enlarged Hilbert spaces, retaining the original operator-domain restrictions. The construction accommodates internal and external ports. We show that the conversions preserve trajectories and the power balance. An incompressible Kelvin--Voigt solid illustrates the results.
ER -