• DocumentCode
    821578
  • Title

    More A_{1}E+EA_{2}=-D and \\dot{X}=A_{1}X+XA_{2}+D,X(0)=C

  • Author

    Lacoss, R.T. ; Shakal, A.F.

  • Author_Institution
    Massachusetts Institute of Technology, Cambridge, MA, USA
  • Volume
    21
  • Issue
    3
  • fYear
    1976
  • fDate
    6/1/1976 12:00:00 AM
  • Firstpage
    405
  • Lastpage
    406
  • Abstract
    The solution of the real matrix equation A_{1}E + EA_{2} = - D is given in terms of the eigenvalues and eigenvectors of A_{1} \\in R^{{n}_{1} \\times n_{1}}, A_{2} \\in R^{n_{2} \\times n_{2}} , and the elements of D . The solution is valid if the Aiare symmetric or if they do not have repeated eigenvalues. The solution can be extended to handle nonsymmetric matrices with repeated eigenvalues. The solution of \\dot{X} = A_{1}X+XA_{2} + D, X(0) = C is also given in closed form for the case of nonrepeated eigenvalues or symmetric Ai.
  • Keywords
    Matrix equations; Numerical integration; Costs; Eigenvalues and eigenfunctions; Equations; Industrial plants; Laboratories; Metalworking machines; Optimal control; Q measurement; Sufficient conditions; Symmetric matrices;
  • fLanguage
    English
  • Journal_Title
    Automatic Control, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9286
  • Type

    jour

  • DOI
    10.1109/TAC.1976.1101249
  • Filename
    1101249
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=821578