A solution of the continuous Lyapunov equation by means of power series

Jan Ježek

Kybernetika (1986)

  • Volume: 22, Issue: 3, page 209-217
  • ISSN: 0023-5954

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Ježek, Jan. "A solution of the continuous Lyapunov equation by means of power series." Kybernetika 22.3 (1986): 209-217. <http://eudml.org/doc/28631>.

@article{Ježek1986,
author = {Ježek, Jan},
journal = {Kybernetika},
keywords = {stationary Lyapunov equation; continuous Lyapunov equation; Taylor expansion},
language = {eng},
number = {3},
pages = {209-217},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A solution of the continuous Lyapunov equation by means of power series},
url = {http://eudml.org/doc/28631},
volume = {22},
year = {1986},
}

TY - JOUR
AU - Ježek, Jan
TI - A solution of the continuous Lyapunov equation by means of power series
JO - Kybernetika
PY - 1986
PB - Institute of Information Theory and Automation AS CR
VL - 22
IS - 3
SP - 209
EP - 217
LA - eng
KW - stationary Lyapunov equation; continuous Lyapunov equation; Taylor expansion
UR - http://eudml.org/doc/28631
ER -

References

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  2. P. Lancaster, Theory of Matrices, Academic Press, New York 1969. (1969) Zbl0186.05301MR0245579
  3. W. Givens, Elementary divisors and some properties of the Lyapunov mapping X → A X + X A * , Argonne National Laboratory, Argonne, Illinois 1961. (1961) 
  4. P. Hagander, Numerical solution of A T S + S A + Q = 0 , Lund Institute of Technology, Division of Automatic Control, Lund, Sweden 1969. (1969) MR0312703
  5. V. Kučera, The matrix equation AX + XB = C, SIAM J. Appl. Math. 26 (1974), 1, 15-25. (1974) MR0340280
  6. M. C. Pease, Methods of Matrix Algebra, Academic Press, New York 1965. (1965) Zbl0145.03701MR0207719
  7. P. Lancaster, Explicit solution of the matrix equations, SIAM Rev. 12 (1970), 544-566. (1970) MR0279115
  8. J. Štěcha A. Kozáčiková, J. Kozáčik, Algorithm for solution of equations P A + A T P = - Q and M T P M - P = - Q resulting in Lyapunov stability analysis of linear systems, Kybernetika 9 (1973), 1, 62-71. (1973) MR0327355
  9. S. Barnett, Remarks on solution of AX + XB = C, Electron. Lett. 7 (1971), p. 385. (1971) MR0319360
  10. C. S. Lu, Solution of the matrix equation AX + XB = C, Electron. Lett. 7 (1971), 185-186. (1971) MR0319359
  11. C. S. Berger, A numerical solution of the matrix equation P = Φ P Φ T + S , IEEE Trans. Automat. Control AC-16 (1971), 4, 381-382. (1971) 
  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. (1968) MR0234974
  13. M. Záruba, The Stationary Solution of the Riccati Equation, (in Czech). ÚTIA ČSAV Research Report 371, Prague 1973. (1973) 
  14. E. C. Ma, A finite series solution of the matrix equation AX - XB = C, SIAM J. Appl. Math. 74 (1966), 490-495. (1966) Zbl0144.27003MR0201456
  15. E. J. Davison, F. T. Man, The numerical solution of A ' Q + Q A = - C , IEEE Trans. Automat. Control AC-13 (1968), 4, 448-449. (1968) MR0235707
  16. A. Trampus, A canonical basis for the matrix transormation X → A X + X B , J. Math. Anal. Appl. 14 (1966), 242-252. (1966) MR0190157
  17. J. Ježek, UTIAPACK - Subroutine Package for Problems of Control Theory. The User's Manual, ÚTIA ČSAV, Prague 1984. (1984) 

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