Estimates of solutions to linear differential equations of neutral type with several delays of argument
Sibirskij žurnal industrialʹnoj matematiki, Tome 16 (2013) no. 3, pp. 53-60.

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider a system of linear differential equations of neutral type with several delays of argument. We obtain conditions on the matrix coefficients of the system under which all its solutions decay exponentially at infinity. Using functionals of Lyapunov–Krasovskii type, we establish uniform estimates of solutions.
Keywords: equations of neutral type, asymptotic stability, Lyapunov–Krasovskii functional.
@article{SJIM_2013_16_3_a4,
     author = {G. V. Demidenko and E. S. Vodop'yanov and M. A. Skvortsova},
     title = {Estimates of solutions to linear differential equations of neutral type with several delays of argument},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {53--60},
     publisher = {mathdoc},
     volume = {16},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2013_16_3_a4/}
}
TY  - JOUR
AU  - G. V. Demidenko
AU  - E. S. Vodop'yanov
AU  - M. A. Skvortsova
TI  - Estimates of solutions to linear differential equations of neutral type with several delays of argument
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2013
SP  - 53
EP  - 60
VL  - 16
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2013_16_3_a4/
LA  - ru
ID  - SJIM_2013_16_3_a4
ER  - 
%0 Journal Article
%A G. V. Demidenko
%A E. S. Vodop'yanov
%A M. A. Skvortsova
%T Estimates of solutions to linear differential equations of neutral type with several delays of argument
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2013
%P 53-60
%V 16
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2013_16_3_a4/
%G ru
%F SJIM_2013_16_3_a4
G. V. Demidenko; E. S. Vodop'yanov; M. A. Skvortsova. Estimates of solutions to linear differential equations of neutral type with several delays of argument. Sibirskij žurnal industrialʹnoj matematiki, Tome 16 (2013) no. 3, pp. 53-60. http://geodesic.mathdoc.fr/item/SJIM_2013_16_3_a4/

[1] Krasovskii N. N., Nekotorye zadachi teorii ustoichivosti dvizheniya, Fizmatgiz, M., 1959 | MR

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

[3] Kheil Dzh., Teoriya funktsionalno-differentsialnykh uravnenii, Mir, M., 1984 | MR

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

[5] Kharitonov V. L., Hinrichsen D., “Exponential estimates for time delay systems”, Systems Control Lett., 53:5 (2004), 395–405 | DOI | MR | Zbl

[6] Kharitonov V. L., Mondié S., Collado J., “Exponential estimates for neutral time-delay systems: an LMI approach”, IEEE Trans. Automat. Control, 50:5 (2005), 666–670 | DOI | MR

[7] Khusainov D. Ya., Ivanov A. F., Kozhametov A. T., “Otsenki skhodimosti reshenii lineinykh statsionarnykh sistem differentsialno-raznostnykh uravnenii s postoyannym zapazdyvaniem”, Differents. uravneniya, 41:8 (2005), 1137–1140 | MR | Zbl

[8] Demidenko G. V., Matveeva I. I., “Asimptoticheskie svoistva reshenii differentsialnykh uravnenii s zapazdyvayuschim argumentom”, Vestnik NGU. Ser. Matematika, mekhanika, informatika, 5:3 (2005), 20–28 | MR | Zbl

[9] Demidenko G. V., Matveeva I. I., “Ustoichivost reshenii differentsialnykh uravnenii s zapazdyvayuschim argumentom i periodicheskimi koeffitsientami v lineinykh chlenakh”, Sib. mat. zhurn., 48:5 (2007), 1025–1040 | MR | Zbl

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

[11] Daletskii Yu. L., Krein M. G., Ustoichivost reshenii differentsialnykh uravnenii v banakhovom prostranstve, Nauka, M., 1970 | MR

[12] Godunov S. K., Sovremennye aspekty lineinoi algebry, Nauch. kniga, Novosibirsk, 1997