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MSC2010 34D05

Stability of the asymptotic quiescent position of perturbed homogeneous nonstationary systems

A. P. Zhabko1, O. G. Tikhomirov2, O. N. Сhizhova3

AnnotationSufficient conditions for the existence of an asymptotic quiescent position for homogeneous non-stationary systems of ordinary differential equations with perturbations in the form of functions that disappear with time are obtained in this article. The method of proof is based on the construction of the Lyapunov function, which satisfies the conditions of the theorem proved by V. I. Zubov for the existence of an asymptotic quiescent position. An example of a system of non-linear and non-stationary ordinary differential equations is considered, which illustrates the obtained results.
Keywordsasymptotic quiescent position, asymptotic stability, non-autonomous differential equations, homogeneous differential equation, almost periodic functions, almost uniform average.

1Aleksei P. Zhabko, Professor, Department of Control Theory, Saint-Petersburg State University (35 Universitetskiy pr., Petergof 198504, Russia), Ph.D. (Physics and Mathematics), ORCID: http://orcid.org/0000-0002-6379-0682, zhabko.apmath.spbu@mail.ru

2Oleg G. Tikhomirov, Associate Professor, Department of Control Theory, Saint-Petersburg State University (35 Universitetskiy pr., Petergof 198504, Russia), Ph.D. (Physics and Mathematics), ORCID: https://orcid.org/0000-0003-2321-5525, olegtikhomirov@mail.ru

3Olga N. Сhizhova, Associate Professor, Department of Control Theory, Saint-Petersburg State University (35 Universitetskiy pr., Petergof 198504, Russia), Ph.D. (Physics and Mathematics), ORCID: http://orcid.org/0000-0001-9251-9915, chizhovolg@yandex.ru

Citation: A. P. Zhabko, O. G. Tikhomirov, O. N. Сhizhova, "[Stability of the asymptotic quiescent position of perturbed homogeneous nonstationary systems]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,20:1 (2018) 13–22 (In Russian)

DOI 10.15507/2079-6900.20.201801.13-22