Geodesic
On the stability of systems of linear differential equations of neutral type with distributed delay
Sibirskij žurnal industrialʹnoj matematiki, Tome 22 (2019) no. 3, pp. 118-127 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider one class of systems of nonautonomous linear differential equations of neutral type with distributed delay. We obtain sufficient conditions for the exponential stability of the zero solution and conditions on perturbations of the coefficients under which the exponential stability of the zero solution is preserved. Using a Lyapunov–Krasovskiĭ functional of a special kind, we prove some estimates that characterize the exponential decay of solutions at infinity.
Keywords: system of neutral type, distributed delay, periodic coefficients, exponential stability, Lyapunov–Krasovskiĭ functional. 
@article{SJIM_2019_22_3_a10,
     author = {T. Yskak},
     title = {On the stability of systems of linear differential equations of neutral type with distributed delay},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {118--127},
     year = {2019},
     volume = {22},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2019_22_3_a10/}
}
TY  - JOUR
AU  - T. Yskak
TI  - On the stability of systems of linear differential equations of neutral type with distributed delay
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2019
SP  - 118
EP  - 127
VL  - 22
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SJIM_2019_22_3_a10/
LA  - ru
ID  - SJIM_2019_22_3_a10
ER  - 
%0 Journal Article
%A T. Yskak
%T On the stability of systems of linear differential equations of neutral type with distributed delay
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2019
%P 118-127
%V 22
%N 3
%U http://geodesic.mathdoc.fr/item/SJIM_2019_22_3_a10/
%G ru
%F SJIM_2019_22_3_a10
T. Yskak. On the stability of systems of linear differential equations of neutral type with distributed delay. Sibirskij žurnal industrialʹnoj matematiki, Tome 22 (2019) no. 3, pp. 118-127. http://geodesic.mathdoc.fr/item/SJIM_2019_22_3_a10/

[1] L. E. Elsgolts, S. B. Norkin, Vvedenie v teoriyu differentsialnykh uravnenii s otklonyayuschimsya argumentom, Nauka, M., 1971

[2] Dzh. Kheil, Teoriya funktsionalno-differentsialnykh uravnenii, Mir, M., 1984

[3] D. G. Korenevskii, Ustoichivost dinamicheskikh sistem pri sluchainykh vozmuscheniyakh parametrov. Algebraicheskie kriterii, Nauk. dumka, Kiev, 1989

[4] N. V. Azbelev, V. P. Maksimov, L. F. Rakhmatullina, Vvedenie v teoriyu funktsionalno-differentsialnykh uravnenii, Nauka, M., 1991 | MR

[5] Yu. F. Dolgii, Ustoichivost periodicheskikh differentsialno-raznostnykh uravnenii, Izd-vo Ural. gos. un-ta, Ekaterinburg, 1996

[6] V. B. Kolmanovskii, A. D. Myshkis, Introduction to the Theory and Applications of Functional Differential Equations, Math. Appl., 463, Kluwer Acad. Publ., Dordrecht, 1999 | MR | Zbl

[7] K. Gu, V. L. Kharitonov, J. Chen, Stability of Time-Delay Systems, Control Engrg., Birkhauser, Boston, 2003 | MR | Zbl

[8] R. P. Agarwal, L. Berezansky, E. Braverman, A. Domoshnitsky, Nonoscillation Theory of Functional Differential Equations with Applications, Springer Verl., N.Y., 2012 | MR | Zbl

[9] M. I. Gil', Stability of neutral functional differential equations, Atlantis Stud. Differ. Equ., 3, Atlantis Press, Paris, 2014 | DOI | MR | Zbl

[10] T. K. Yskak, “Ob ustoichivosti reshenii differentsialnykh uravnenii neitralnogo tipa s raspredelennym zapazdyvaniem”, Izvestiya IGU. Ser. Matematika, 25 (2018), 159–169 | MR | Zbl

[11] G. V. Demidenko, “Stability of solutions to linear differential equations of neutral type”, J. Anal. Appl., 7:3 (2009), 119–130 | MR | Zbl

[12] G. V. Demidenko, T. V. Kotova, M. A. Skvortsova, “Ustoichivost reshenii differentsialnykh uravnenii neitralnogo tipa”, Vestn. NGU. Ser. Matematika, mekhanika, informatika, 10:3 (2010), 17–29 | MR | Zbl

[13] G. V. Demidenko, E. S. Vodopyanov, M. A. Skvortsova, “Otsenki reshenii lineinykh differentsialnykh uravnenii neitralnogo tipa s neskolkimi otkloneniyami argumenta”, Sib. zhurn. industr. matematiki, 16:3 (2013), 53–60 | Zbl

[14] G. V. Demidenko, I. I. Matveeva, “Ob otsenkakh reshenii sistem differentsialnykh uravnenii neitralnogo tipa s periodicheskimi koeffitsientami”, Sib. mat. zhurn., 55:5 (2014), 1059–1077 | MR

[15] T. K. Yskak, “Dostatochnye usloviya asimptoticheskoi ustoichivosti reshenii odnogo klassa lineinykh sistem neitralnogo tipa s periodicheskimi koeffitsientami”, Dinamicheskie sistemy, 5(33):3–4 (2015), 177–191 | Zbl

[16] I. I. Matveeva, “Ob eksponentsialnoi ustoichivosti reshenii periodicheskikh sistem neitralnogo tipa”, Sib. mat. zhurn., 58:2 (2017), 344–352 | MR | Zbl

[17] I. I. Matveeva, “O robastnoi ustoichivosti reshenii periodicheskikh sistem neitralnogo tipa”, Sib. zhurn. industr. matematiki, 21:4 (2018), 86–95 | Zbl

[18] T. K. Yskak, “Stability of solutions to systems of differential equations with distributed delay”, Funct. Differ. Equ., 25:1–2 (2018), 97–108 | MR