• DocumentCode
    1541015
  • Title

    Strong Stability of an Unstable Wave Equation by Boundary Feedback With Only Displacement Observation

  • Author

    Guo, Wei ; Shao, Zhi-Chao

  • Author_Institution
    Sch. of Inf. Technol. & Manage., Univ. of Int. Bus. & Econ., Beijing, China
  • Volume
    57
  • Issue
    9
  • fYear
    2012
  • Firstpage
    2367
  • Lastpage
    2372
  • Abstract
    The stabilization of a 1-D wave equation that contains instability at its free end and control at the other end is considered. The controller is designed through the estimated state that is designed in the case that only displacement is available. The method of “backstepping” is adopted in investigation. The C0 -semigroup theory and Lyapunov method are used to show that the closed-loop system is asymptotically stable.
  • Keywords
    Lyapunov methods; asymptotic stability; closed loop systems; feedback; group theory; state estimation; wave equations; 1D wave equation; C0-semigroup theory; Lyapunov method; asymptotic stability; backstepping method; boundary feedback; closed loop system; displacement observation; state estimation; unstable wave equation stability; Asymptotic stability; Backstepping; Displacement measurement; Eigenvalues and eigenfunctions; Equations; Observers; Propagation; Backstepping; boundary control; distributed parameter system; vibrating string;
  • fLanguage
    English
  • Journal_Title
    Automatic Control, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9286
  • Type

    jour

  • DOI
    10.1109/TAC.2012.2204837
  • Filename
    6218171
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1541015