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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 
 

 

Conditions of stability for periodic linear systems of ordinary differential equations


Author: V. I. Slyn′ko
Translated by: S. Yu. Pilyugin
Original publication: Algebra i Analiz, tom 30 (2018), nomer 5.
Journal: St. Petersburg Math. J. 30 (2019), 885-900
MSC (2010): Primary 34D20
DOI: https://doi.org/10.1090/spmj/1575
Published electronically: July 26, 2019
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Abstract: Stability for periodic linear systems is studied by a new method based on ideas and approaches of commutator calculus. The study of stability for periodic linear system of differential equations is reduced to the study of stability for a periodic linear system with constant coefficients and impulse response.

Sufficient conditions of asymptotic stability are obtained for the initial periodic linear system. They are based on a theorem of the Lyapunov direct method for differential equations with impulse response. Asymptotic stability is also studied for a periodic linear system under small violations of the Lappo-Danilevskiĭ conditions.


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Additional Information

V. I. Slyn′ko
Affiliation: S. P. Timoshenko Mechanics Institute of the National Academy of Sciences of Ukraine ul. Nesterova, 3, Kiev, 03057, Ukraine
Email: vitstab@ukr.net

DOI: https://doi.org/10.1090/spmj/1575
Keywords: Linear periodic system, stability, commutator calculus, linear impulsive system, direct Lyapunov method
Received by editor(s): July 15, 2017
Published electronically: July 26, 2019
Additional Notes: This research was supported in part by the Ministry of Education and Science of Ukraine (project 0116U004691) and by the State Foundation for Fundamental Research of Ukraine (project F62/110-2015 no. 0112U000241)
Article copyright: © Copyright 2019 American Mathematical Society