• DocumentCode
    764033
  • Title

    On the stability of coupled delay differential and continuous time difference equations

  • Author

    Pepe, Pierdomenico ; Verriest, Erik I.

  • Author_Institution
    Dipt. di Ingegneria Elettrica, Univ. degli Studi dell´´Aquila, L´´Aquila, Italy
  • Volume
    48
  • Issue
    8
  • fYear
    2003
  • Firstpage
    1422
  • Lastpage
    1427
  • Abstract
    A Lyapunov-type stability analysis for coupled delay differential and continuous time difference equations is given. Such systems are encountered as the internal dynamics of input output linearized nonlinear time delay systems. They appear also in lossless propagation models, economics and gas dynamics. The main contribution of this note is a two-step algorithm for the stability analysis of such systems. At the first step, only the L2 stability is checked; while at the second step, the Lyapunov stability of the difference part of the system is analyzed. In these two steps, the stability of the whole system can be checked. Using this method, we show the stability of a system (dependent on the delay), for which the known methods in literature are inconclusive.
  • Keywords
    asymptotic stability; control system analysis; delay-differential systems; difference equations; nonlinear systems; Lyapunov stability; Lyapunov-Krasovskii methodology; asymptotic stability; continuous time difference equations; delay differential equations; internal dynamics; nonlinear systems; time delay systems; Asymptotic stability; Couplings; Delay effects; Delay lines; Delay systems; Difference equations; Lyapunov method; Nonlinear dynamical systems; Propagation losses; Stability analysis;
  • fLanguage
    English
  • Journal_Title
    Automatic Control, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9286
  • Type

    jour

  • DOI
    10.1109/TAC.2003.815036
  • Filename
    1220760