English

Lyapunov characterization of boundedness of reachability sets for infinite-dimensional systems

Optimization and Control 2026-03-05 v1 Systems and Control Systems and Control Dynamical Systems

Abstract

We prove a converse Lyapunov theorem for boundedness of reachability sets for a general class of control systems whose flow is Lipschitz continuous on compact intervals with respect to trajectory-dominated inputs. We show that this condition is satisfied by many semi-linear evolution equations. For ordinary differential equations, as a consequence of our results, we obtain a converse Lyapunov theorem for forward completeness, without a priori restrictions on the magnitude of inputs.

Keywords

Cite

@article{arxiv.2603.04190,
  title  = {Lyapunov characterization of boundedness of reachability sets for infinite-dimensional systems},
  author = {Patrick Bachmann and Andrii Mironchenko},
  journal= {arXiv preprint arXiv:2603.04190},
  year   = {2026}
}