Lyapunov functions obtained from first order approximations

2015/11/20 by V Andrieu, Andrieu, V
Engineering · Mathematics · #Control and Stability of Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Biology Tumor Growth #Stability and Controllability of Differential Equations

paper · doi:10.48550/arxiv.1511.06588

openalex publication_date 2015/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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