no. 3-4
Ordinary Differential Equations/Automation (theoretical)
Eigenvalues and eigenvectors assignment for neutral type systems
[Placement de valeurs propres et de vecteurs propres pour un système avec retard de type neutre]

Présenté par : the Editorial Board

Sklyar, Katerina1 ; Rabah, Rabah2 ; Sklyar, Grigory1
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
Comptes Rendus. Mathématique, Tome 351 (2013) no. 3-4, pp. 91-95.

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.

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.

Reçu le :
Accepté le :
Publié le :
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 
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Sklyar, Katerina; Rabah, Rabah; Sklyar, Grigory. Eigenvalues and eigenvectors assignment for neutral type systems. Comptes Rendus. Mathématique, Tome 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

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