Application of Lyapunov's Direct Method to the Study of the Stability of Solutions to Systems of Impulsive Differential Equations
Matematičeskie zametki, Tome 96 (2014) no. 1, pp. 22-35.

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

Classical theorems on the stability of the solutions of impulsive differential equations are further developed.
Keywords: impulsive differential equation, Lyapunov's direct method, Lyapunov (asymptotic) stability, Cauchy problem, equilibrium state stability, Hahn function class.
@article{MZM_2014_96_1_a2,
     author = {A. I. Dvirnyj and V. I. Slyn'ko},
     title = {Application of {Lyapunov's} {Direct} {Method} to the {Study} of the {Stability} of {Solutions} to {Systems} of {Impulsive} {Differential} {Equations}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {22--35},
     publisher = {mathdoc},
     volume = {96},
     number = {1},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_96_1_a2/}
}
TY  - JOUR
AU  - A. I. Dvirnyj
AU  - V. I. Slyn'ko
TI  - Application of Lyapunov's Direct Method to the Study of the Stability of Solutions to Systems of Impulsive Differential Equations
JO  - Matematičeskie zametki
PY  - 2014
SP  - 22
EP  - 35
VL  - 96
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2014_96_1_a2/
LA  - ru
ID  - MZM_2014_96_1_a2
ER  - 
%0 Journal Article
%A A. I. Dvirnyj
%A V. I. Slyn'ko
%T Application of Lyapunov's Direct Method to the Study of the Stability of Solutions to Systems of Impulsive Differential Equations
%J Matematičeskie zametki
%D 2014
%P 22-35
%V 96
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2014_96_1_a2/
%G ru
%F MZM_2014_96_1_a2
A. I. Dvirnyj; V. I. Slyn'ko. Application of Lyapunov's Direct Method to the Study of the Stability of Solutions to Systems of Impulsive Differential Equations. Matematičeskie zametki, Tome 96 (2014) no. 1, pp. 22-35. http://geodesic.mathdoc.fr/item/MZM_2014_96_1_a2/

[1] A. M. Samoilenko, N. A. Perestyuk, Differentsialnye uravneniya s impulsnym vozdeistviem, Vischa shkola, K., 1987

[2] V. Lakshmikantham, D. D. Bainov, P. S. Simeonov, Theory of Impulsive Differential Equations, Ser. Modern Appl. Math., 6, World Sci. Publ., Singapore, 1989 | MR | Zbl

[3] X. Liu, A. Willms, “Stability analysis and applications to large scale impulsive systems: a new approach”, Canad. Appl. Math. Quart., 3:4 (1995), 419–444 | MR | Zbl

[4] M. O. Perestyuk, O. S. Chernikova, “Some modern aspects of the theory of impulsive differential equations”, Ukrainian Math. J., 60, no. 1, 91–107 | MR | Zbl

[5] N. A. Perestyuk, “K voprosu ustoichivosti polozheniya ravnovesiya impulsnykh sistem”, Godishn. vissh. uchebni zaved. Prilozh. matem., 1:1 (1975), 145–151

[6] A. O. Ignatev, O. A. Ignatev, A. A. Soliman, “Ob asimptoticheskoi ustoichivosti i neustoichivosti reshenii sistem s impulsnym vozdeistviem”, Matem. zametki, 80:4 (2006), 516–525 | DOI | MR | Zbl

[7] A. O. Ignatyev, “On the stability of invariant sets of systems with impulse effect”, Nonlinear Anal., 69:1 (2008), 53–72 | DOI | MR | Zbl

[8] A. O. Ignatyev, O. A. Ignatyev, “Stability of Solutions of Systems with Impulse Effect”, Progress in Nonlinear Analysis Research, Nova Sci. Publ., New York, 2009, 363–389 | MR

[9] R. I. Gladilina, A. O. Ignatev, “Ob ustoichivosti periodicheskikh sistem s impulsnym vozdeistviem”, Matem. zametki, 76:1 (2004), 44–51 | DOI | MR | Zbl

[10] A. A. Martynyuk, V. I. Slynko, “Ob ustoichivosti dvizheniya nelineinoi impulsnoi sistemy”, Prikl. mekh., 40:2 (2004), 134–144 | MR | Zbl

[11] A. A. Martynyuk, V. Lakshmikantam, S. Lila, Ustoichivost dvizheniya: metod integralnykh neravenstv, Naukova dumka, K., 1989 | MR

[12] W. Hahn, Stability of Motion, Grundlehren Math. Wiss., 138, Springer-Verlag, Berlin, 1967 | MR

[13] V. I. Slynko, “Lineinye matrichnye neravenstva i ustoichivost dvizheniya impulsnykh sistem”, Dop. NAN Ukraïni, 2008, no. 4, 68–71 | MR | Zbl

[14] V. S. Denisenko, “Ustoichivost nechetkikh impulsnykh sistem Takagi–Sugeno: metod lineinykh matrichnykh neravenstv”, Dop. NAN Ukraïni, 2008, no. 11, 66–73 | MR

[15] V. S. Denisenko, V. I. Slynko, “Impulsnaya stabilizatsiya mekhanicheskikh sistem dlya modelei Takagi–Sugeno”, Prikl. mekh., 45:10 (2009), 115–130 | MR | Zbl

[16] A. I. Dvirnyi, V. I. Slynko, “Ustoichivost reshenii differentsialnykh uravnenii s impulsnym vozdeistviem v kriticheskikh sluchayakh”, Sib. matem. zhurn., 52:1 (2011), 70–80 | MR | Zbl