• DocumentCode
    391035
  • Title

    Stability of planar switched systems: the linear single, input case

  • Author

    Boscain, Ugo

  • Author_Institution
    SISSA-ISAS, Trieste, Italy
  • Volume
    3
  • fYear
    2002
  • fDate
    10-13 Dec. 2002
  • Firstpage
    3312
  • Abstract
    We study the stability of the origin for the dynamical system, x˙(t)=u(t)Ax(t)+(1-u(t))Bx(t), where A and B are two 2×2 real matrices with eigenvalues having strictly negative real part, x∈R2 and u(.):[0, ∞[→ [0, 1] is a completely random measurable function. More precisely, we find a (coordinates invariant) necessary and sufficient condition on A and B for the origin to be asymptotically stable for each function u(.). This bidimensional problem assumes particular interest since linear systems of higher dimensions can be reduced to our situation. Two unpublished examples in the (more difficult) case in which both matrices have real eigenvalues are analyzed in details.
  • Keywords
    asymptotic stability; eigenvalues and eigenfunctions; linear systems; matrix algebra; bidimensional problem; completely random measurable function; dynamical system; eigenvalues; linear systems; matrices; negative real part; planar switched systems stability; real eigenvalues; real matrices; Algebra; Asymptotic stability; Computer aided software engineering; Eigenvalues and eigenfunctions; Gold; Linear systems; Predictive models; Switched systems; Transmission line matrix methods;
  • fLanguage
    English
  • Publisher
    ieee
  • Conference_Titel
    Decision and Control, 2002, Proceedings of the 41st IEEE Conference on
  • ISSN
    0191-2216
  • Print_ISBN
    0-7803-7516-5
  • Type

    conf

  • DOI
    10.1109/CDC.2002.1184385
  • Filename
    1184385