• DocumentCode
    2253454
  • Title

    Necessary and sufficient conditions for common quadratic Lyapunov functions for a pair of stable LTI systems whose system matrices are in companion form

  • Author

    Shorten, Robert N. ; Narendra, Kumpati S.

  • Author_Institution
    Hamilton Inst., Nat. Univ. of Ireland, Maynooth, Ireland
  • Volume
    6
  • fYear
    2003
  • fDate
    4-6 June 2003
  • Firstpage
    5203
  • Abstract
    In this paper the problem of determining necessary and sufficient conditions for the Lyapunov function for a pair of stable linear time-invariant systems whose system matrices, A1, A2, are in companion form is considered. It is shown that a necessary and sufficient condition for the existence of such a function is that the matrix product A1A2 does not have an eigenvalue that is real and negative. Examples are presented to illustrate the result.
  • Keywords
    Lyapunov methods; eigenvalues and eigenfunctions; linear matrix inequalities; linear systems; common quadratic Lyapunov functions; companion form; eigenvalue; linear time-invariant systems; stable LTI systems; system matrices; Artificial intelligence; Control systems; Eigenvalues and eigenfunctions; Linear matrix inequalities; Lyapunov method; Polynomials; Sufficient conditions;
  • fLanguage
    English
  • Publisher
    ieee
  • Conference_Titel
    American Control Conference, 2003. Proceedings of the 2003
  • ISSN
    0743-1619
  • Print_ISBN
    0-7803-7896-2
  • Type

    conf

  • DOI
    10.1109/ACC.2003.1242553
  • Filename
    1242553
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=2253454