• DocumentCode
    835588
  • Title

    The discrete Lyapunov equation in controllable canonical form

  • Author

    Ptak, Vlastimil

  • Author_Institution
    Czechoslovakia Academy of Sciences, Praha, Czechoslovakia
  • Volume
    26
  • Issue
    2
  • fYear
    1981
  • fDate
    4/1/1981 12:00:00 AM
  • Firstpage
    580
  • Lastpage
    581
  • Abstract
    A new method of treating Lyapunov equations is proposed. If D and D^{-} are two self-adjoint one-dimensional matrices related in a certain way, then X-C^{\\ast }XC=D if and only if X^{-1}-CX^{-1} C^{\\ast }=D^{-} . As an application, a generalization of a recent result is given. If f is the vector f=(0,0...,0,1)^{T} , then the solution of X-CXC^{\\ast } = ff^{\\ast } is shown to be inverse of the Schur-Cohn matrix.
  • Keywords
    Lyapunov matrix equations; Equations; Feature extraction; Linear predictive coding; Parameter estimation; Polynomials; Speech processing; State estimation;
  • fLanguage
    English
  • Journal_Title
    Automatic Control, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9286
  • Type

    jour

  • DOI
    10.1109/TAC.1981.1102644
  • Filename
    1102644
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=835588