Koopman Framework for Global stability analysis

Alexandre Mauroy, Aivar Sootla, Igor Mezić

Research output: Contribution in Book/Catalog/Report/Conference proceedingChapter (peer-reviewed)peer-review

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.

Original languageEnglish
Title of host publicationThe Koopman Operator in Systems and Control
Subtitle of host publicationConcepts, Methodologies, and Applications
EditorsAlexandre Mauroy, Igor Mezic, Yoshihiko Susuki
PublisherSpringer
Chapter2
Pages35-58
Number of pages24
ISBN (Electronic)978-3-030-35713-9
ISBN (Print)978-3-030-35712-2
DOIs
Publication statusPublished - 1 Jan 2020

Publication series

NameLecture Notes in Control and Information Sciences
Volume484
ISSN (Print)0170-8643
ISSN (Electronic)1610-7411

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