• DocumentCode
    824853
  • Title

    The numerical solution of \\dot{X} = A_{1}X + XA_{2} + D, X(0) = C

  • Author

    Hoskins, William ; Walton, Dave

  • Author_Institution
    University of Manitoba, Winnipeg, Canada
  • Volume
    22
  • Issue
    5
  • fYear
    1977
  • fDate
    10/1/1977 12:00:00 AM
  • Firstpage
    881
  • Lastpage
    882
  • Abstract
    An improved method of solving the general matrix differential equation \\dot{X} = A_{1}X + XA_{2} + D, X(0) = C for X is considered where A1and A2are stable matrices. The algorithm proposed requires only 5n^{2} words of memory and converges in approximately 43n^{3} \\mu s where μ is the multiplication time of the digital computer and n = \\max (n_{1},n_{2}) where A_{1} \\in R^{n_{1} \\times n_{1}}, A_{2} \\in R^{n_{2} \\times n_{2}} . The algorithm is extremely simple to implement.
  • Keywords
    Differential equations; Matrix equations; Numerical integration; Artificial intelligence; Controllability; Differential equations; Lyapunov method; Nonlinear dynamical systems; Nonlinear equations; Poisson equations; Stochastic processes; Stochastic systems; Sufficient conditions;
  • fLanguage
    English
  • Journal_Title
    Automatic Control, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9286
  • Type

    jour

  • DOI
    10.1109/TAC.1977.1101588
  • Filename
    1101588
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=824853