Geodesic
The asymptotic stability of a~nonstationary system with delay
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2013), pp. 24-33.

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In this paper we study the exponential stability of a linear system of differential equations with a constant delay such that the right-hand side of one of its subsystems contains the multiplier in the form of an exponent. We establish sufficient conditions for the existence of an asymptotically periodic solution to the inhomogeneous system.
Keywords: asymptotic stability, exponential bound, asymptotically periodic solution. 
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B. G. Grebenshchikov. The asymptotic stability of a~nonstationary system with delay. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2013), pp. 24-33. http://geodesic.mathdoc.fr/item/IVM_2013_8_a2/

[1] Barbashin E. A., Vvedenie v teoriyu ustoichivosti, M., 1967

[2] Grebenschikov B. G., “Asimptoticheskoe povedenie reshenii odnoi sistemy s lineinym zapazdyvaniem”, Izv. RAN. Teoriya i sistemy upravleniya, 2008, no. 2, 29–34

[3] Grebenschikov B. G., Novikov S. I., “O neustoichivosti nekotoroi sistemy s lineinym zapazdyvaniem”, Izv. vuzov. Matem., 2010, no. 2, 3–13 | MR | Zbl

[4] Grebenschikov B. G., “Ob ustoichivosti po pervomu priblizheniyu odnoi nestatsionarnoi sistemy s zapazdyvaniem”, Izv. vuzov. Matem., 2012, no. 2, 34–42

[5] Bellman R., Kuk K., Differentsialno-raznostnye uravneniya, M., 1967 | MR

[6] Fikhtengolts G. M., Kurs differentsialnogo i integralnogo ischisleniya, v. 3, M., 1966

[7] Mitropolskii Yu. A., Metod usredneniya v nelineinoi mekhanike, Kiev, 1971

[8] Bylov B. F., Vinograd R. E., Grobman D. M., Nemytskii V. V., Teoriya pokazatelei Lyapunova i ee prilozhenie k voprosam ustoichivosti, M., 1967

[9] Grebenschikov B. G., “O suschestvovanii asimptoticheski periodicheskogo resheniya odnoi sistemy s zapazdyvaniem”, Izv. Uralsk. gos. un-ta, 2003, no. 26, Matematika i mekhanika. Vyp. 5, 44–54

[10] Khalanai A., Veksler D., Kachestvennaya teoriya impulsnykh sistem, M., 1971