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}
}