• DocumentCode
    798814
  • Title

    Stability conditions for an n th-order nonlinear time-varying differential system

  • Author

    Man, F. ; Davison, E.

  • Author_Institution
    University of Toronto, Toronto, Ontario, Canada
  • Volume
    13
  • Issue
    6
  • fYear
    1968
  • fDate
    12/1/1968 12:00:00 AM
  • Firstpage
    723
  • Lastpage
    724
  • Abstract
    The stability of a system described by the n th-order differential equation y^(n) + a_{n-1}Y^(n-1) + ... + a_{1}\\dot{Y} + a_{0}y = 0 where a_{i} = a_{i}(t, y, \\dot{y}, ... , y^(n-1)) , i = 0,1,2, ... , n-1 is considered. It is shown that if the instantaneous roots of the characteristic equation of the system are always contained in a circle on the complex plane with center ( - z, 0 ), z > 0 and radius ω such that frac{z}{\\Omega } > {{1, n = 1}{\\sqrt {2n(n-1)}, n \\geq 2} then the system is uniformly asymptotically stable in the sense of Liapunov.
  • Keywords
    Nonlinear systems, time-varying; Stability; Time-varying systems, nonlinear; Asymptotic stability; Circuit stability; Differential equations; Nonlinear equations; Stability criteria; Sufficient conditions; Time varying systems; Veins;
  • fLanguage
    English
  • Journal_Title
    Automatic Control, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9286
  • Type

    jour

  • DOI
    10.1109/TAC.1968.1099030
  • Filename
    1099030
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=798814