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de Souza, Eurice; Bhattacharyya, S. P.

Controllability, observability and the solution of AX-XB=C. (English) Zbl 0468.15012

Linear Algebra Appl. 39, 167-188 (1981).
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Cited in 1 Review
Cited in 61 Documents

MSC:

15A24 Matrix equations and identities

Keywords:

controllability, observability and the solution of AX-XB=C

Software:

Algorithm 432
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\textit{E. de Souza} and \textit{S. P. Bhattacharyya}, Linear Algebra Appl. 39, 167--188 (1981; Zbl 0468.15012)
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References:

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[2] Gantmacher, F.R., The theory of matrices, (1960), Chelsea, New York · Zbl 0088.25103
[3] 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
[4] Jameson, A., Solution of the equation AX+XB = C by inversion of an M X M or N X N matrix, SIAM J. appl. math., 16, 1020-1023, (1968) · Zbl 0169.35202
[5] Bickart, T.A., Direct solution method for A1E+EA2 = -D, IEEE trans. automatic control, 22, 467-471, (1977)
[6] Smith, R.A., Matrix calculations for Lyapunov quadratic forms, J. differential equations, 2, 208-217, (1966) · Zbl 0151.02206
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[9] Kuc̆era, V., The matrix equation AX+XB = C, SIAM J. appl. math., 26, 15-25, (1974) · Zbl 0245.15004
[10] Wonham, W.M., Linear multivariable control—A geometric approach, (1979), Springer New York · Zbl 0393.93024
[11] Hearon, J.Z., Nonsingular solutions of TA-BT = C, Linear algebra and appl., 16, 57-83, (1977) · Zbl 0368.15007
[12] Wimmer, H.K., Inertia theorems for matrices, controllability and linear vibrations, Linear algebra and appl., 8, 337-343, (1974) · Zbl 0288.15015
[13] Carlson, D.H.; Datta, B.N., The Lyapunov matrix equation SA + A*S = S*B*BS, Linear algebra and appl., 28, 43-52, (1979) · Zbl 0422.15010
[14] Carlson, D.H.; Hill, Richard D., Controllability and inertia theory for functions of a matrix, Linear algebra and appl., 15, 260-266, (1977) · Zbl 0359.15009
[15] Snyders, J.; Zakai, M., On nonnegative solutions of the equation AD+DA’ = -C, SIAM J. appl. math., 18, 704-715, (1970) · Zbl 0203.33401
[16] Antsaklis, P.J., Cyclicity and controllability in linear time invariant systems, IEEE trans. automatic control, 23, 745-746, (1978) · Zbl 0382.93005
[17] Luenberger, D.G., An introduction to observers, IEEE trans. automatic control, 16, 596-602, (1971)
[18] Hautus, M.L.J., Controllability and observability conditions for linear autonomous systems, Nederl. akad. wetensch. proc. ser. A, 72, 443-448, (1969) · Zbl 0188.46801
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.