@inbook{1b1d20a69bce465fb84901d80ab10e47,
title = "Koopman Framework for Global stability analysis",
abstract = "In this chapter, we present a new framework to study global stability of nonlinear systems. The proposed approach is based on the stability properties of the Koopman operator and can be seen as an extension of classic stability analysis of linear systems. In the case of (hyperbolic) equilibria, we show that the existence of specific eigenfunctions of the operator is a necessary and sufficient condition for global stability of the attractor. Moreover, using the realization of the operator in a finite-dimensional basis, we provide a systematic method to compute candidate Lyapunov functions of stable systems.",
author = "Alexandre Mauroy and Aivar Sootla and Igor Mezi{\'c}",
year = "2020",
month = jan,
day = "1",
doi = "10.1007/978-3-030-35713-9_2",
language = "English",
isbn = "978-3-030-35712-2",
series = "Lecture Notes in Control and Information Sciences",
publisher = "Springer",
pages = "35--58",
editor = "Alexandre Mauroy and Igor Mezic and Yoshihiko Susuki",
booktitle = "The Koopman Operator in Systems and Control",
}