• DocumentCode
    2482739
  • Title

    Strict positive realness and the existence of diagonal Lyapunov functions

  • Author

    Shorten, Robert N. ; Narendra, Kumpati S.

  • Author_Institution
    Hamilton Inst., Nat. Univ. of Ireland, Maynooth
  • fYear
    2006
  • fDate
    13-15 Dec. 2006
  • Firstpage
    2918
  • Lastpage
    2923
  • Abstract
    The problem of determining whether or not a stable LTI dynamical system has a Lyapunov function V(x) = xTPx, with a diagonal matrix P > 0, referred to as a diagonal Lyapunov function, has attracted a great deal of attention in the past. The results obtained thus far are, for the most part, algebraic in nature. In this paper, using a geometric approach, and the concept of common Lyapunov functions, necessary and sufficient conditions for the existence of a diagonal Lyapunov function are given in terms of strict positive realness of a transfer function matrix
  • Keywords
    Lyapunov matrix equations; linear systems; stability; transfer function matrices; LTI dynamical system; diagonal Lyapunov functions; diagonal matrix; strict positive realness; system stability; transfer function matrix; Differential equations; Lyapunov method; Stability; Sufficient conditions; Symmetric matrices; Transfer functions; USA Councils;
  • fLanguage
    English
  • Publisher
    ieee
  • Conference_Titel
    Decision and Control, 2006 45th IEEE Conference on
  • Conference_Location
    San Diego, CA
  • Print_ISBN
    1-4244-0171-2
  • Type

    conf

  • DOI
    10.1109/CDC.2006.376934
  • Filename
    4177972
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=2482739