WSEAS Transactions on Mathematics

Print ISSN: 1109-2769
E-ISSN: 2224-2880

Volume 17, 2018

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of WSEAS Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.

Volume 17, 2018

On Rank One Perturbations of Hamiltonian System with Periodic Coefficients

AUTHORS: Mouhamadou Dosso, Arouna G. Y. Traore, Jean-Claude Koua Brou

Download as PDF

From a theory developed by C. Mehl, et al., a theory of the rank one perturbation of Hamiltonian systems with periodic coefficients is proposed. It is showed that the rank one perturbation of the fundamental solution of Hamiltonian system with periodic coefficients is solution of its rank one perturbation. Some results on the consequences of the strong stability of these types of systems on their rank one perturbation is proposed. Two numerical examples are given to illustrate this theory. 2010 Mathematics Subject Classification : 15A63, 15A21, 47A55, 93B10, 93C73.

KEYWORDS: Eigenvalue, symplectic matrix, Hamiltonian system, Fundamental solutions, Perturbation


[1] C. Brezinski, Computational Aspercts of Linear Control, Kluwer Academic Publishers, 2002.

[2] M. Dosso, Sur quelques algorithms d’analyse de stabilité forte de matrices symplectiques, PHD Thesis (September 2006), Université de Bretagne Occidentale. Ecole Doctorale SMIS, Laboratoire de Mathématiques, UFR Sciences et Techniques.

[3] M. Dosso, N. Coulibaly, An Analysis of the Behavior of Mulpliers of Hamiltonian System with periodic. Far East Journal of Mathematical Sciences. Vol. 99, Number 3, 2016, 301–322.

[4] M. Dosso, N. Coulibaly, Symplectic matrices and strong stability of Hamiltonian systems with periodic coefficients. Journal of Mathematical Sciences : Advances and Applications. Vol. 28, 2014, Pages 15–38.

[5] M. Dosso, N. Coulibaly and L. Samassi, Strong stability of symplectic matrices using a spectral dichotomy method. Far East Journal of Applied Mathematics. Vol. 79, Number 2, 2013, pp. 73– 110.

[6] M. Dosso and M. Sadkane. On the strong stability of symplectic matrices. Numerical Linear Algebra with Applications, 20(2) (2013), 234–249.

[7] M. Dosso, M. Sadkane, A spectral trichotomy method for symplectic matrices, Numer Algor. 52(2009), 187–212

[8] S.K. Godunov, Verification of boundedness for the powers of symplectic matrices with the help of averaging, Siber. Math. J. 33,(1992), 939– 949.

[9] S.K. Godunov, M. Sadkane, Numerical determination of a canonical form of a symplectic matrix, Siberian Math. J. 42(2001), 629–647.

[10] S.K. Godunov, M. Sadkane, Spectral analysis of symplectic matrices with application to the theory of parametric resonance, SIAM J. Matrix Anal. Appl. 28(2006), 1083–1096.

[11] B. Hassibi, A. H. Sayed, T. Kailath, IndefiniteQuadratic Estimation and Control, SIAM, Philadelphia, PA, 1999.

[12] P. Lancaster, L. Rodman, Algebraic Riccati Equations, Clarendon Press, 1995.

[13] C. Mehl, V. Mehrmann, A.C.M. Ran, and L. Rodman. Eigenvalue perturbation theory under generic rank one perturbations: Symplectic, orthogonal, and unitary matrices. BIT, 54(2014), 219–255.

[14] C. Mehl, V. Mehrmann, A.C.M. Ran and L. Rodman. Eigenvalue perturbation theory of classes of structured matrices under generic structured rank one perturbations. Linear Algebra Appl., 435(2011), 687–716.

[15] V.A., Yakubovich, V.M. Starzhinskii, Linear differential equations with periodic coefficients, Vol. 1 & 2., Wiley, New York (1975)

[16] YAN Qing-you. The properties of a kind of random symplectic matrices. Applied mathematics and Mechanics. Vol 23, No 5, May 2002.

WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 17, 2018, Art. #46, pp. 377-384

Copyright Β© 2018 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution License 4.0

Bulletin Board


The editorial board is accepting papers.

WSEAS Main Site