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.
Accepté le :
Publié le :
@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://archive.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://archive.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://archive.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, Tome 351 (2013) no. 3-4, pp. 91-95. doi : 10.1016/j.crma.2013.02.007. http://archive.numdam.org/articles/10.1016/j.crma.2013.02.007/
[1] Families of Exponentials, Cambridge University Press, Cambridge, 1995
[2] Introduction to Functional–Differential Equations, Applied Mathematical Sciences, vol. 99, Springer-Verlag, New York, 1993
[3] 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] Stability and stabilizability of mixed retarded-neutral type systems, ESAIM Control Optim. Calc. Var., Volume 18 (2012), pp. 656-692
[5] 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] Stability analysis of neutral type systems in Hilbert space, J. Differ. Equations, Volume 214 (2005) no. 2, pp. 391-428
Cité par Sources :