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On matrix equations $X - AXF = C$ and $X - A\overline{X}F = C$. (English) Zbl 05580666

15A24Matrix equations and identities
Full Text: DOI
[1] Bartels, R. H.; Stewart, G. W.: A solution of the equation AX+XB=C, Commun. ACM 15, 820-826 (1972)
[2] Kitagawa, G.: An algorithm for solving the matrix equation X=FXFT+S., Int. J. Control 25, 745-753 (1977) · Zbl 0364.65025 · doi:10.1080/00207177708922266
[3] Kleinman, D. L.; Rao, P. K.: Extensions to the bartels--stewart algorithm for linear matrix equation, IEEE trans. Automat. control 23, No. 1, 85-87 (1978) · Zbl 0369.65005 · doi:10.1109/TAC.1978.1101681
[4] Golub, G.; Nash, S.; Van Loan, C.: A Hessenberg--Schur method for the problem AX+XB=C, IEEE trans. Automat. control 24, 909-913 (1979) · Zbl 0421.65022 · doi:10.1109/TAC.1979.1102170
[5] Betser, A.; Cohen, N.; Zeheb, E.: On solving the Lyapunov and Stein equations for a companion matrix, System control lett. 25, 211-218 (1995) · Zbl 0877.93043 · doi:10.1016/0167-6911(94)00072-4
[6] Ma, E. C.: A finite series solution of the matrix equation AX-XB=C, SIAM J. Appl. math. 14, 490-495 (1966) · Zbl 0144.27003 · doi:10.1137/0114043
[7] Brockett, R. W.: Introduction to matrix analysis, (1970)
[8] Young, N. J.: Formulae for the solution of Lyapunov matrix equation, Internat. J. Control 31, 159-179 (1980) · Zbl 0432.93050 · doi:10.1080/00207178008961035
[9] Desouza, E.; Bhattacharyya, S.: Controllability and observability and the solution of AX-XB=C, Linear algebra appl. 39, 167-188 (1981) · Zbl 0468.15012 · doi:10.1016/0024-3795(81)90301-3
[10] Zhou, B.; Duan, G. R.: An explicit solution to the matrix equation AX-XF=BY, Linear algebra appl. 402, 345-366 (2005) · Zbl 1076.15016 · doi:10.1016/j.laa.2005.01.018
[11] Jones, J.; Charleslew, J. R.: Solutions of the Lyapunov matrix equation BX-XA=C., IEEE trans. Automat. control 27, No. 2, 464-466 (1982)
[12] Hanzon, B.: A Faddeev sequence method for solving Lyapunov and Sylvester equations, Linear algebra appl., 401-430 (1996) · Zbl 0859.65038 · doi:10.1016/0024-3795(95)00683-4
[13] Jameson, A.: Solution of the equation AX-XB=C by inversion of an $M{\times}$M or $N{\times}$N matrix, SIAM J. Appl. math. 16, 1020-1023 (1968) · Zbl 0169.35202 · doi:10.1137/0116083
[14] Jiang, T.; Wei, M.: On solutions of the matrix equations X-AXB=C and X-ax\bar{}b=C, Linear algebra appl. 367, 225-233 (2003) · Zbl 1019.15002 · doi:10.1016/S0024-3795(02)00633-X
[15] Wu, A. G.; Duan, G. R.: Solution to the generalized Sylvester matrix equation AV+BW=EVF, IET control theory appl. 1, No. 1, 402-408 (2007)
[16] Wu, A. G.; Fu, Y. M.; Duan, G. R.: On solutions of the matrix equations V-AVF=BW and V-av\bar{}f=BW, Math. comput. Modelling 47, 1181-1197 (2008) · Zbl 1145.15302 · doi:10.1016/j.mcm.2007.06.024
[17] Lewis, F. L.: Further remarks on the Cayley--Hamilton theorem and leverrier’s method for matrix pencil (sE-A), IEEE trans. Automat. control 31, No. 9, 869-870 (1986) · Zbl 0601.15010 · doi:10.1109/TAC.1986.1104420