Factorizations and partial contraction of nonlinear systems

M. A. Belabbas, J. J.E. Slotine

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, we introduce new results in the analysis of convergence of nonlinear systems. The point of view we take is the one of contraction theory and we focus in particular on convergence to smooth manifolds. A main characteristic of contraction theory is that it does not require nor use any knowledge about the asymptotic trajectory of the system. Our contribution is to extend the core body of contraction results to include such knowledge in the analysis. As a result, this approach naturally leads to the definition of a new type of commutator for vector fields. We will show that the vanishing of this commutator, together with a contraction assumption, yields a sufficient condition for convergence and we will illustrate the results on the Andronov-Hopf oscillator.

Original languageEnglish (US)
Title of host publicationProceedings of the 2010 American Control Conference, ACC 2010
Pages3440-3445
Number of pages6
StatePublished - Oct 15 2010
Externally publishedYes
Event2010 American Control Conference, ACC 2010 - Baltimore, MD, United States
Duration: Jun 30 2010Jul 2 2010

Publication series

NameProceedings of the 2010 American Control Conference, ACC 2010

Other

Other2010 American Control Conference, ACC 2010
CountryUnited States
CityBaltimore, MD
Period6/30/107/2/10

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ASJC Scopus subject areas

  • Control and Systems Engineering

Cite this

Belabbas, M. A., & Slotine, J. J. E. (2010). Factorizations and partial contraction of nonlinear systems. In Proceedings of the 2010 American Control Conference, ACC 2010 (pp. 3440-3445). [5531088] (Proceedings of the 2010 American Control Conference, ACC 2010).