• DocumentCode
    810950
  • Title

    Improving the predictions of the circle criterion by combining quadratic forms

  • Author

    Power, H.M. ; Tsoi, A.C.

  • Author_Institution
    University of Salford, Salford, England
  • Volume
    18
  • Issue
    1
  • fYear
    1973
  • fDate
    2/1/1973 12:00:00 AM
  • Firstpage
    65
  • Lastpage
    67
  • Abstract
    By using a Lyapunov function which consists of different quadratic forms in various sectors of the ( u, (du/d\\tau ) ) plane, the prediction of the circle criterion that the null solution of (d^{2}u/d\\tau ^{2}) + 2(du/d\\tau ) + f(\\tau , u, (du/d\\tau ))\\cdotp u = 0 is asymptotically stable for 0 \\leq \\alpha < f(\\cdotp) < \\beta , with \\beta = (\\sqrt {\\alpha } + 2)^{2} , is improved to \\beta = [{frac{(\\sqrt {\\alpha } + 1)^{2} + 1 + \\sqrt {(\\sqrt {\\alpha } + 1)^{4} + 2 (\\sqrt {\\alpha } + 1)^{2} + 5}}{2}}^{frac{1}{2}} + 1 ]^{2} .
  • Keywords
    Asymptotic stability; Circle stability criterion; Lyapunov functions; Nonlinear systems, time-varying; Time-varying systems, nonlinear; Algebra; Equations; Lyapunov method;
  • fLanguage
    English
  • Journal_Title
    Automatic Control, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9286
  • Type

    jour

  • DOI
    10.1109/TAC.1973.1100204
  • Filename
    1100204
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=810950