• DocumentCode
    50221
  • Title

    A Differential Lyapunov Framework for Contraction Analysis

  • Author

    Forni, F. ; Sepulchre, R.

  • Author_Institution
    Dept. of Electr. Eng. & Comput. Sci., Univ. of Liege, Liège, Belgium
  • Volume
    59
  • Issue
    3
  • fYear
    2014
  • fDate
    Mar-14
  • Firstpage
    614
  • Lastpage
    628
  • Abstract
    Lyapunov´s second theorem is an essential tool for stability analysis of differential equations. The paper provides an analog theorem for incremental stability analysis by lifting the Lyapunov function to the tangent bundle. The Lyapunov function endows the state-space with a Finsler structure. Incremental stability is inferred from infinitesimal contraction of the Finsler metrics through integration along solutions curves.
  • Keywords
    Lyapunov methods; differential equations; stability; state-space methods; Finsler structure; Lyapunov second theorem; analog theorem; differential Lyapunov framework; differential equations; incremental stability analysis; infinitesimal contraction; state-space; tangent bundle; Asymptotic stability; Differential equations; Lyapunov methods; Manifolds; Measurement; Stability analysis; Vectors; Contraction; Lyapunov methods; incremental stability; linearization; nonlinear systems;
  • fLanguage
    English
  • Journal_Title
    Automatic Control, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9286
  • Type

    jour

  • DOI
    10.1109/TAC.2013.2285771
  • Filename
    6632882
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=50221