Lyapunov functions obtained from first order approximations
Dynamical Systems
2015-11-23 v1
Abstract
In this paper, we study the construction of Lyapunov functions based on first order approximations. In a first part, the study of local exponential stability property of a transverse invariant manifold is considered. This part is mainly a rephrasing of the result of [3]. It is shown with this framework how to construct a Lyapunov function which characterizes this local stability property. In a second part, when considering the global stability property of an equilibrium point it is shown that the study of first order approximation along solutions of the system allows to construct a Lyapunov function.
Cite
@article{arxiv.1511.06588,
title = {Lyapunov functions obtained from first order approximations},
author = {V Andrieu},
journal= {arXiv preprint arXiv:1511.06588},
year = {2015}
}