메뉴 건너뛰기




Volumn 230, Issue 2, 2009, Pages 690-698

On matrix equations X - A X F = C and X - A over(X, -) F = C

Author keywords

Controllability matrix; Kronecker map; Observability matrix; Real representation

Indexed keywords

COMPLEX MATRICES; CONTROLLABILITY MATRICES; CONTROLLABILITY MATRIX; EXPLICIT SOLUTIONS; KRONECKER MAP; MATRIX EQUATIONS; OBSERVABILITY MATRIX; REAL REPRESENTATION; SYMMETRIC OPERATORS;

EID: 67349254484     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2009.01.013     Document Type: Article
Times cited : (37)

References (17)
  • 1
    • 84976855597 scopus 로고
    • A solution of the equation A X + X B = C
    • Bartels R.H., and Stewart G.W. A solution of the equation A X + X B = C. Commun. ACM 15 (1972) 820-826
    • (1972) Commun. ACM , vol.15 , pp. 820-826
    • Bartels, R.H.1    Stewart, G.W.2
  • 3
    • 0017930740 scopus 로고
    • Extensions to the Bartels-Stewart algorithm for linear matrix equation
    • Kleinman D.L., and Rao P.K. Extensions to the Bartels-Stewart algorithm for linear matrix equation. IEEE Trans. Automat. Control 23 1 (1978) 85-87
    • (1978) IEEE Trans. Automat. Control , vol.23 , Issue.1 , pp. 85-87
    • Kleinman, D.L.1    Rao, P.K.2
  • 4
    • 0018721357 scopus 로고
    • A Hessenberg-Schur method for the problem A X + X B = C
    • Golub G., Nash S., and Van Loan C. A Hessenberg-Schur method for the problem A X + X B = C. IEEE Trans. Automat. Control 24 (1979) 909-913
    • (1979) IEEE Trans. Automat. Control , vol.24 , pp. 909-913
    • Golub, G.1    Nash, S.2    Van Loan, C.3
  • 5
    • 0029640096 scopus 로고
    • On solving the Lyapunov and Stein equations for a companion matrix
    • Betser A., Cohen N., and Zeheb E. On solving the Lyapunov and Stein equations for a companion matrix. System Control Lett. 25 (1995) 211-218
    • (1995) System Control Lett. , vol.25 , pp. 211-218
    • Betser, A.1    Cohen, N.2    Zeheb, E.3
  • 6
    • 0039616736 scopus 로고
    • A finite series solution of the matrix equation A X - X B = C
    • Ma E.C. A finite series solution of the matrix equation A X - X B = C. SIAM. J. Appl. Math. 14 (1966) 490-495
    • (1966) SIAM. J. Appl. Math. , vol.14 , pp. 490-495
    • Ma, E.C.1
  • 8
    • 0018973513 scopus 로고
    • Formulae for the solution of Lyapunov matrix equation
    • Young N.J. Formulae for the solution of Lyapunov matrix equation. Internat. J. Control 31 (1980) 159-179
    • (1980) Internat. J. Control , vol.31 , pp. 159-179
    • Young, N.J.1
  • 9
    • 0000875808 scopus 로고
    • Controllability and observability and the solution of A X - X B = C
    • DeSouza E., and Bhattacharyya S. Controllability and observability and the solution of A X - X B = C. Linear Algebra Appl. 39 (1981) 167-188
    • (1981) Linear Algebra Appl. , vol.39 , pp. 167-188
    • DeSouza, E.1    Bhattacharyya, S.2
  • 10
    • 17744390556 scopus 로고    scopus 로고
    • An explicit solution to the matrix equation A X - X F = B Y
    • Zhou B., and Duan G.R. An explicit solution to the matrix equation A X - X F = B Y. Linear Algebra Appl. 402 (2005) 345-366
    • (2005) Linear Algebra Appl. , vol.402 , pp. 345-366
    • Zhou, B.1    Duan, G.R.2
  • 11
    • 0020112884 scopus 로고
    • Solutions of the Lyapunov matrix equation B X - X A = C.
    • Jones J., and Charleslew J.R. Solutions of the Lyapunov matrix equation B X - X A = C. IEEE Trans. Automat. Control 27 2 (1982) 464-466
    • (1982) IEEE Trans. Automat. Control , vol.27 , Issue.2 , pp. 464-466
    • Jones, J.1    Charleslew, J.R.2
  • 12
    • 4243553355 scopus 로고    scopus 로고
    • A faddeev sequence method for solving Lyapunov and Sylvester equations
    • Hanzon B. A faddeev sequence method for solving Lyapunov and Sylvester equations. Linear Algebra Appl. (1996) 401-430
    • (1996) Linear Algebra Appl. , pp. 401-430
    • Hanzon, B.1
  • 13
    • 0040773836 scopus 로고
    • Solution of the equation A X - X B = C by inversion of an M × M or N × N matrix
    • Jameson A. Solution of the equation A X - X B = C by inversion of an M × M or N × N matrix. SIAM J. Appl. Math. 16 (1968) 1020-1023
    • (1968) SIAM J. Appl. Math. , vol.16 , pp. 1020-1023
    • Jameson, A.1
  • 14
    • 0037720091 scopus 로고    scopus 로고
    • On solutions of the matrix equations X - A X B = C and X - A over(X, ̄) B = C
    • Jiang T., and Wei M. On solutions of the matrix equations X - A X B = C and X - A over(X, ̄) B = C. Linear Algebra Appl. 367 (2003) 225-233
    • (2003) Linear Algebra Appl. , vol.367 , pp. 225-233
    • Jiang, T.1    Wei, M.2
  • 15
    • 33846238423 scopus 로고    scopus 로고
    • Solution to the generalized Sylvester matrix equation A V + B W = E V F
    • Wu A.G., and Duan G.R. Solution to the generalized Sylvester matrix equation A V + B W = E V F. IET Control Theory Appl. 1 1 (2007) 402-408
    • (2007) IET Control Theory Appl. , vol.1 , Issue.1 , pp. 402-408
    • Wu, A.G.1    Duan, G.R.2
  • 16
    • 42749083362 scopus 로고    scopus 로고
    • On solutions of the matrix equations V - A V F = B W and V - A over(V, ̄) F = B W
    • Wu A.G., Fu Y.M., and Duan G.R. On solutions of the matrix equations V - A V F = B W and V - A over(V, ̄) F = B W. Math. Comput. Modelling 47 (2008) 1181-1197
    • (2008) Math. Comput. Modelling , vol.47 , pp. 1181-1197
    • Wu, A.G.1    Fu, Y.M.2    Duan, G.R.3
  • 17
    • 0022783875 scopus 로고
    • Further remarks on the Cayley-Hamilton theorem and Leverrier's method for matrix pencil (s E - A)
    • Lewis F.L. Further remarks on the Cayley-Hamilton theorem and Leverrier's method for matrix pencil (s E - A). IEEE Trans. Automat. Control 31 9 (1986) 869-870
    • (1986) IEEE Trans. Automat. Control , vol.31 , Issue.9 , pp. 869-870
    • Lewis, F.L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.