Conditions of stability for periodic linear systems of ordinary differential equations

Slyn′ko, V.

doi:10.1090/spmj/1575

Conditions of stability for periodic linear systems of ordinary differential equations
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by 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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