Ordinary Differential Equations/Automation (theoretical)
Eigenvalues and eigenvectors assignment for neutral type systems
Comptes Rendus. Mathématique, Volume 351 (2013) no. 3-4, pp. 91-95.

For a class of linear neutral type systems, the problem of eigenvalues and eigenvectors assignment is investigated, i.e. the system that has the given spectrum and almost all, in some sense, eigenvectors is investigated. The result is used for the analysis of the critical number of solvability of a vector moment problem.

Pour une classe de systèmes linéaire avec retards de type neutre, on étudie le problème de placement de valeurs et de vecteurs propres à un nombre de vecteurs près. Le résultat est utilisé pour analyser lʼintervalle critique de solvabilité dʼun problème de moments vectoriel.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2013.02.007
Sklyar, Katerina 1; Rabah, Rabah 2; Sklyar, Grigory 1

1 Institute of Mathematics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland
2 IRCCyN/École des mines de Nantes, 4, rue Alfred-Kastler, BP 20722, 44307 Nantes cedex 3, France
@article{CRMATH_2013__351_3-4_91_0,
     author = {Sklyar, Katerina and Rabah, Rabah and Sklyar, Grigory},
     title = {Eigenvalues and eigenvectors assignment for neutral type systems},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {91--95},
     publisher = {Elsevier},
     volume = {351},
     number = {3-4},
     year = {2013},
     doi = {10.1016/j.crma.2013.02.007},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2013.02.007/}
}
TY  - JOUR
AU  - Sklyar, Katerina
AU  - Rabah, Rabah
AU  - Sklyar, Grigory
TI  - Eigenvalues and eigenvectors assignment for neutral type systems
JO  - Comptes Rendus. Mathématique
PY  - 2013
SP  - 91
EP  - 95
VL  - 351
IS  - 3-4
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2013.02.007/
DO  - 10.1016/j.crma.2013.02.007
LA  - en
ID  - CRMATH_2013__351_3-4_91_0
ER  - 
%0 Journal Article
%A Sklyar, Katerina
%A Rabah, Rabah
%A Sklyar, Grigory
%T Eigenvalues and eigenvectors assignment for neutral type systems
%J Comptes Rendus. Mathématique
%D 2013
%P 91-95
%V 351
%N 3-4
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2013.02.007/
%R 10.1016/j.crma.2013.02.007
%G en
%F CRMATH_2013__351_3-4_91_0
Sklyar, Katerina; Rabah, Rabah; Sklyar, Grigory. Eigenvalues and eigenvectors assignment for neutral type systems. Comptes Rendus. Mathématique, Volume 351 (2013) no. 3-4, pp. 91-95. doi : 10.1016/j.crma.2013.02.007. http://www.numdam.org/articles/10.1016/j.crma.2013.02.007/

[1] Avdonin, Sergei A.; Ivanov, Sergei A. Families of Exponentials, Cambridge University Press, Cambridge, 1995

[2] Hale, Jack K.; Verduyn Lunel, Sjoerd M. Introduction to Functional–Differential Equations, Applied Mathematical Sciences, vol. 99, Springer-Verlag, New York, 1993

[3] Rabah, R.; Sklyar, G.M. The analysis of exact controllability of neutral-type systems by the moment problem approach, SIAM J. Control Optim., Volume 46 (2007) no. 6, pp. 2148-2181

[4] Rabah, R.; Sklyar, G.M.; Barkhayev, P.Yu. Stability and stabilizability of mixed retarded-neutral type systems, ESAIM Control Optim. Calc. Var., Volume 18 (2012), pp. 656-692

[5] Rabah, R.; Sklyar, G.M.; Rezounenko, A.V. Generalized Riesz basis property in the analysis of neutral type systems, C. R. Acad. Sci. Paris, Ser. I, Volume 337 (2003) no. 1, pp. 19-24

[6] Rabah, R.; Sklyar, G.M.; Rezounenko, A.V. Stability analysis of neutral type systems in Hilbert space, J. Differ. Equations, Volume 214 (2005) no. 2, pp. 391-428

Cited by Sources: