• DocumentCode
    807531
  • Title

    Instability of slowly varying systems

  • Author

    Skoog, Ronald A. ; Lau, Clifford G Y

  • Author_Institution
    Bell Telephone Laboratories, Holmdel, NJ, USA
  • Volume
    17
  • Issue
    1
  • fYear
    1972
  • fDate
    2/1/1972 12:00:00 AM
  • Firstpage
    86
  • Lastpage
    92
  • Abstract
    Instability criteria are obtained for systems described by \\dot{x} = A(t)x when the parameters are slowly varying. In particular it is shown that, when A(t) has eigenvalues in the right-half plane and all eigenvalues are bounded away from the imaginary axis, then if sup_{t \\geq 0} \\parallel \\dot{A}(t)\\parallel is sufficiently small, the system has unbounded solutions. Results are also given for systems of the form \\dot{x} = A(t)x + f(x, t) , and the dichotomy of solutions is studied in both the linear and nonlinear cases.
  • Keywords
    Linear systems, time-varying continuous-time; Stability; Eigenvalues and eigenfunctions; Equations; Laboratories; Lyapunov method; Nonlinear systems; Stability criteria; Vectors;
  • fLanguage
    English
  • Journal_Title
    Automatic Control, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9286
  • Type

    jour

  • DOI
    10.1109/TAC.1972.1099866
  • Filename
    1099866
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=807531