Converse Lyapunov theorems for control systems with unbounded controls
Optimization and Control
2021-09-10 v1
Abstract
In this paper, we extend well-known relationships between global asymptotic controllability, sample stabilizability, and the existence of a control Lyapunov function to a wide class of control systems with unbounded controls, which includes control-polynomial systems. In particular, we consider open loop controls and discontinuous stabilizing feedbacks, which may be unbounded approaching the target, so that the corresponding trajectories may present a chattering behavior. A key point of our results is to prove that global asymptotic controllability, sample stabilizability, and existence of a control Lyapunov function for these systems or for an {\em impulsive extension} of them are equivalent.
Cite
@article{arxiv.2109.04126,
title = {Converse Lyapunov theorems for control systems with unbounded controls},
author = {Anna Chiara Lai and Monica Motta},
journal= {arXiv preprint arXiv:2109.04126},
year = {2021}
}