Conditions of stability for periodic linear systems of ordinary differential equations
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V. I. Slyn′ko
Translated by: S. Yu. Pilyugin - St. Petersburg Math. J. 30 (2019), 885-900
- 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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Bibliographic 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
- 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)
- © Copyright 2019 American Mathematical Society
- Journal: St. Petersburg Math. J. 30 (2019), 885-900
- MSC (2010): Primary 34D20
- DOI: https://doi.org/10.1090/spmj/1575
- MathSciNet review: 3856106