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# Article

 Title: A solution of the continuous Lyapunov equation by means of power series (English) Author: Ježek, Jan Language: English Journal: Kybernetika ISSN: 0023-5954 Volume: 22 Issue: 3 Year: 1986 Pages: 209-217 . Category: math . MSC: 15A24 MSC: 34D20 MSC: 39B20 MSC: 65F30 MSC: 65K10 MSC: 93C30 MSC: 93D05 idZBL: Zbl 0631.65073 idMR: MR852322 . Date available: 2009-09-24T17:53:15Z Last updated: 2012-06-05 Stable URL: http://hdl.handle.net/10338.dmlcz/125476 . Reference: [1] F. R. Gantmacher: The Theory of Matrices.vol. 1. Chelsea, New York 1966. MR 1657129 Reference: [2] P. Lancaster: Theory of Matrices.Academic Press, New York 1969. Zbl 0186.05301, MR 0245579 Reference: [3] W. Givens: Elementary divisors and some properties of the Lyapunov mapping $X \rightarrow AX + XA^*$.Argonne National Laboratory, Argonne, Illinois 1961. Reference: [4] P. Hagander: Numerical solution of $A^T S + SA + Q = 0$.Lund Institute of Technology, Division of Automatic Control, Lund, Sweden 1969. MR 0312703 Reference: [5] V. Kučera: The matrix equation AX + XB = C.SIAM J. Appl. Math. 26 (1974), 1, 15-25. MR 0340280 Reference: [6] M. C. Pease: Methods of Matrix Algebra.Academic Press, New York 1965. Zbl 0145.03701, MR 0207719 Reference: [7] P. Lancaster: Explicit solution of the matrix equations.SIAM Rev. 12 (1970), 544-566. MR 0279115 Reference: [8] J. Štěcha A. Kozáčiková, J. Kozáčik: Algorithm for solution of equations $PA + A^T P = -Q$ and $M^T PM - P= -Q$ resulting in Lyapunov stability analysis of linear systems.Kybernetika 9 (1973), 1, 62-71. MR 0327355 Reference: [9] S. Barnett: Remarks on solution of AX + XB = C.Electron. Lett. 7 (1971), p. 385. MR 0319360 Reference: [10] C. S. Lu: Solution of the matrix equation AX + XB = C.Electron. Lett. 7 (1971), 185-186. MR 0319359 Reference: [11] C. S. Berger: A numerical solution of the matrix equation $P= \Phi P \Phi^T + S$.IEEE Trans. Automat. Control AC-16 (1971), 4, 381-382. Reference: [12] A. Jameson: Solution of the equation AX + XB = C by inversion of an M x M or N X N matrix.SIAM J. Appl. Math. 16 (1968), 1020-1023. MR 0234974 Reference: [13] M. Záruba: The Stationary Solution of the Riccati Equation.(in Czech). ÚTIA ČSAV Research Report 371, Prague 1973. Reference: [14] E. C. Ma: A finite series solution of the matrix equation AX - XB = C.SIAM J. Appl. Math. 74 (1966), 490-495. Zbl 0144.27003, MR 0201456 Reference: [15] E. J. Davison, F. T. Man: The numerical solution of $A'Q + QA = - C$.IEEE Trans. Automat. Control AC-13 (1968), 4, 448-449. MR 0235707 Reference: [16] A. Trampus: A canonical basis for the matrix transormation $X \rightarrow AX+ XB$.J. Math. Anal. Appl. 14 (1966), 242-252. MR 0190157 Reference: [17] J. Ježek: UTIAPACK - Subroutine Package for Problems of Control Theory. The User's Manual.ÚTIA ČSAV, Prague 1984. .

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