PreprintCC0arXiv
Robust forms for passive descriptor systems
Abstract
We show how to compute the passivity radius of a given generalized state-space model of a rational transfer function that represents a passive system, both in the continuous-time and discrete-time cases. We then use this to construct robust descriptor realizations. For the continuous-time case, these realizations have a port-Hamiltonian descriptor form. For the discrete-time case a similar result holds for the so-called normalized realizations. The computation of such robust realizations is linked in both these cases to a particular solution of a linear matrix inequality that characterizes the passivity of the transfer function.
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BibTeX
@misc{benner2026robust,
title = {{Robust forms for passive descriptor systems}},
author = {Peter Benner and Anshul Prajapati and Paul Van Dooren},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.39465},
eprint = {2609.39465},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39465},
note = {CC0},
}
RIS
TY - UNPB
TI - Robust forms for passive descriptor systems
AU - Peter Benner
AU - Anshul Prajapati
AU - Paul Van Dooren
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.39465
UR - https://arxiv.org/abs/2609.39465
AB - We show how to compute the passivity radius of a given generalized state-space model of a rational transfer function that represents a passive system, both in the continuous-time and discrete-time cases. We then use this to construct robust descriptor realizations. For the continuous-time case, these realizations have a port-Hamiltonian descriptor form. For the discrete-time case a similar result holds for the so-called normalized realizations. The computation of such robust realizations is linked in both these cases to a particular solution of a linear matrix inequality that characterizes the passivity of the transfer function.
ER -