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.
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