Abstract
This paper presents an investigation of the asymptotic stability of a linear system of ordinary differential equations in which the principal part is a Jordan matrix with variable coefficients and the perturbation matrix can have an arbitrary structure.
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N. I. Gavrilov, Methods in the Theory of Ordinary Differential Equations [in Russian], Moscow (1962).
I. M. Rapoport, Some Asymptotic Methods in the Theory of Ordinary Differential Equations [in Russian], Kiev (1954).
B. F. Bylov et al., Theory of the Lyapunov Index [in Russian], Moscow (1966).
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Translated from Matematicheskie Zametki, Vol. 8, No. 6, pp. 761–772, December, 1970.
The author wishes to thank A. A. Abramov for his interest in this work and for his many useful suggestions.
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Voblyi, V.A. A condition for the asymptotic stability of a linear homogeneous system whose principal part is a Jordan matrix. Mathematical Notes of the Academy of Sciences of the USSR 8, 900–906 (1970). https://doi.org/10.1007/BF01673691
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DOI: https://doi.org/10.1007/BF01673691