| 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. |
| . |
