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PreprintCC BY-NC-ND 4.0arXiv

Real and complex stability radii for a class of transport networks

  • Anthony Hastir
  • Birgit Jacob
  • Hannes Wagener
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Abstract

We characterize stability and its robustness for a class of boundary controlled, boundary observed hyperbolic partial differential equations. In particular, we show that asymptotic and exponential stability coincide for this class. Furthermore, we introduce the real and complex stability radii for which we give explicit formulas. In addition, we consider the dual system and its application to controllability and observability. Our main results are illustrated with two examples.

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Cite

BibTeXRIS
BibTeX
@misc{hastir2026real,
  title = {{Real and complex stability radii for a class of transport networks}},
  author = {Anthony Hastir and Birgit Jacob and Hannes Wagener},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.12812},
  eprint = {2607.12812},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.12812},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Real and complex stability radii for a class of transport networks
AU  - Anthony Hastir
AU  - Birgit Jacob
AU  - Hannes Wagener
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2607.12812
UR  - https://arxiv.org/abs/2607.12812
AB  - We characterize stability and its robustness for a class of boundary controlled, boundary observed hyperbolic partial differential equations. In particular, we show that asymptotic and exponential stability coincide for this class. Furthermore, we introduce the real and complex stability radii for which we give explicit formulas. In addition, we consider the dual system and its application to controllability and observability. Our main results are illustrated with two examples.
ER  -