Global Stability Analysis Using the Eigenfunctions of the Koopman Operator

Alexandre Mauroy, Igor Mezić

Research output: Contribution to journalArticlepeer-review

Abstract

We propose a novel operator-theoretic framework to study global stability of nonlinear systems. Based on the spectral properties of the so-called Koopman operator, our approach can be regarded as a natural extension of classic linear stability analysis to nonlinear systems. The main results establish the (necessary and sufficient) relationship between the existence of specific eigenfunctions of the Koopman operator and the global stability property of hyperbolic fixed points and limit cycles. These results are complemented with numerical methods which are used to estimate the region of attraction of the fixed point or to prove in a systematic way global stability of the attractor within a given region of the state space.

Original languageEnglish
Article number7384725
Pages (from-to)3356-3369
Number of pages14
JournalIEEE Transactions on Automatic Control
Volume61
Issue number11
DOIs
Publication statusPublished - 1 Nov 2016
Externally publishedYes

Keywords

  • Global stability
  • Koopman operator
  • spectral methods

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