Geodesic
On a characteristic of asymptotic stability of solutions to linear systems with periodic coefficients
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 8 (2008) no. 3, pp. 60-80 
Yu. Yu. Klevtsova. On a characteristic of asymptotic stability of solutions to linear systems with periodic coefficients. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 8 (2008) no. 3, pp. 60-80. http://geodesic.mathdoc.fr/item/VNGU_2008_8_3_a3/
@article{VNGU_2008_8_3_a3,
     author = {Yu. Yu. Klevtsova},
     title = {On a characteristic of asymptotic stability of solutions to linear systems with periodic coefficients},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {60--80},
     year = {2008},
     volume = {8},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2008_8_3_a3/}
}
TY  - JOUR
AU  - Yu. Yu. Klevtsova
TI  - On a characteristic of asymptotic stability of solutions to linear systems with periodic coefficients
JO  - Sibirskij žurnal čistoj i prikladnoj matematiki
PY  - 2008
SP  - 60
EP  - 80
VL  - 8
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VNGU_2008_8_3_a3/
LA  - ru
ID  - VNGU_2008_8_3_a3
ER  - 
%0 Journal Article
%A Yu. Yu. Klevtsova
%T On a characteristic of asymptotic stability of solutions to linear systems with periodic coefficients
%J Sibirskij žurnal čistoj i prikladnoj matematiki
%D 2008
%P 60-80
%V 8
%N 3
%U http://geodesic.mathdoc.fr/item/VNGU_2008_8_3_a3/
%G ru
%F VNGU_2008_8_3_a3

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

We consider a characteristic of asymptotic stability of solutions to linear systems with periodic coefficients. We suggest a way for calculating this characteristic. Taking it as a principle we elaborated an algorithm for numerical investigation of asymptotic stability of zero solution to linear systems with periodic coefficients.

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

[2] Yakubovich V. A., Starzhinskii V. M., Lineinye differentsialnye uravneniya s periodicheskimi koeffitsientami i ikh prilozheniya, Nauka, M., 1972 | MR

[3] Uilkson Dzh., Algebraicheskaya problema sobstvennykh znachenii, Nauka, M., 1970

[4] Godunov S. K., Lektsii po sovremennym aspektam lineinoi algebry, Nauchnaya kniga, Novosibirsk, 2002

[5] Demidenko G. V., Matveeva I. I., “Ob ustoichivosti reshenii lineinykh sistem s periodicheskimi koeffitsientami”, Sib. mat. zhurn., 42:2 (2001), 332–348 | MR | Zbl

[6] Demidenko G. V., Matveeva I. I., “Ob ustoichivosti reshenii kvazilineinykh periodicheskikh sistem differentsialnykh uravnenii”, Sib. mat. zhurn., 45:6 (2004), 1271–1284 | MR | Zbl

[7] Godunov S. K., Obyknovennye differentsialnye uravneniya s postoyannymi koeffitsientami, v. 1, Kraevye zadachi, Novosibirsk, 1994

[8] Bulgakov A. Ya., “Effektivno vychislyaemyi parametr kachestva ustoichivosti sistem lineinykh differentsialnykh uravnenii s postoyannymi koeffitsientami”, Sib. mat. zhurn., 21:3 (1980), 32–41 | MR | Zbl

[9] Klevtsova Yu. Yu., “O chislennom issledovanii asimptoticheskoi ustoichivosti lineinykh sistem s periodicheskimi koeffitsientami”, Sib. zhurn. industr. mat., 8:2 (22) (2005), 103–115

[10] Pavlov B. V., Povzner A. Ya., “Ob odnom metode chislennogo integrirovaniya sistem obyknovennykh differentsialnykh uravnenii”, Zhurn. vych. mat. i mat. fiziki, 13:4 (1973), 1056–1059 | MR | Zbl

[11] Moler C., Van Loan C., “Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-five Years Later”, SIAM Rev., 45:1 (2003), 3–49 | DOI | MR | Zbl

[12] Demidovich B. P., Lektsii po matematicheskoi teorii ustoichivosti, Izd-vo Mosk. un-ta, M., 1998 | MR