• DocumentCode
    809550
  • Title

    Equivalent predictions of the circle criterion and an optimum quadratic form for a second-order system

  • Author

    Tsoi, A. ; Power, H.

  • Author_Institution
    University of Salford, Salford, England
  • Volume
    17
  • Issue
    4
  • fYear
    1972
  • fDate
    8/1/1972 12:00:00 AM
  • Firstpage
    565
  • Lastpage
    566
  • Abstract
    It is shown that, for the equation frac{d^{2}u}{dt^{2}} + \\mu frac{du}{dt} + g (t,u,frac{du}{dt}) {u + \\lambda frac{du}{dt}} = 0 , the maximum value of β for which asymptotic stability can be guaranteed with a < g(t, u, du/dt) < \\beta (a \\geq 0) is the same whether derived by the circle criterion or by means of a quadratic Lyapunov function with constant coefficients, and this maximum value is explicitly evaluated.
  • Keywords
    Asymptotic stability; Circle stability criterion; Lyapunov methods; Nonlinear systems, time-varying; Time-varying systems, nonlinear; Asymptotic stability; Automatic control; Differential equations; Feedback; Functional analysis; Lyapunov method; Nonlinear equations; Stability analysis; Stability criteria; Time varying systems;
  • fLanguage
    English
  • Journal_Title
    Automatic Control, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9286
  • Type

    jour

  • DOI
    10.1109/TAC.1972.1100066
  • Filename
    1100066
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=809550