Lyapunov functions obtained from first order approximations

V Andrieu (1, 2)

1 LAGEP - Laboratoire d'automatique et de génie des procédés
2 Arbeitsgruppe Funktionalanalysis

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.

Domaines: Systèmes dynamiques [math.DS]; Automatique / Robotique

V Andrieu. Lyapunov functions obtained from first order approximations. Control Subject to Computational and Communication Constraints, 474, pp.151-179, 2018. ⟨hal-01231456⟩