Real and complex stability radii for a class of transport networks

Anthony Hastir; Birgit Jacob; Hannes Wagener

Real and complex stability radii for a class of transport networks

Optimization and Control 2026-07-14 v1 Functional Analysis

Authors: Anthony Hastir , Birgit Jacob , Hannes Wagener

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.

Keywords

stability radii transport networks hyperbolic partial differential equations boundary control boundary observation controllability observability

Cite

@article{arxiv.2607.12812,
  title  = {Real and complex stability radii for a class of transport networks},
  author = {Anthony Hastir and Birgit Jacob and Hannes Wagener},
  journal= {arXiv preprint arXiv:2607.12812},
  year   = {2026}
}