• DocumentCode
    824993
  • Title

    A numerical algorithm to solve A^{T}XA - X = Q

  • Author

    Barraud, A.Y.

  • Author_Institution
    Institut National Polytechnique de Grenoble, Grenoble, France
  • Volume
    22
  • Issue
    5
  • fYear
    1977
  • fDate
    10/1/1977 12:00:00 AM
  • Firstpage
    883
  • Lastpage
    885
  • Abstract
    Two kinds of algorithms are usually resorted to in order to solve the well-known Lyapounov discrete equation A^{T}XA - X = Q : transformation of the original linear system in a classical one with n(n + 1)/2 unknowns, and iterative scheme [1]. The first requires n^{4}/4 storage words and a cost of n^{6}/3 multiplications, which is impractical with a large system, and the second applies only if A is a stable matrix. The solution proposed requires no stability assumption and operates in only some n2words and n3multiplications.
  • Keywords
    Lyapunov matrix equations; Control system analysis; Costs; Differential equations; Iterative algorithms; Kalman filters; Linear systems; Maximum likelihood detection; Partial differential equations; Prediction theory; Stability;
  • fLanguage
    English
  • Journal_Title
    Automatic Control, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9286
  • Type

    jour

  • DOI
    10.1109/TAC.1977.1101604
  • Filename
    1101604
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=824993