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arXiv · 2603.04190

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

Patrick Bachmann·Andrii Mironchenko
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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.

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Patrick Bachmann, Andrii Mironchenko. 2026-03-04. Lyapunov characterization of boundedness of reachability sets for infinite-dimensional systems. https://arxiv.org/abs/2603.04190

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