Abstract
It is shown that any linear system of homogeneous differential equations is Lyapunov equivalent to a system of the same order with piecewise constant coefficients, while a system with a uniformly small perturbation is Lyapunov equivalent to the same system with a piecewise constant perturbation of the same small magnitude.
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References
B. F. Bylov, R. E. Vinograd, D.M. Grobman, and V. V. Nemytskii, The Theory of Lyapunov Exponents and Its Applications to the Problems of Stability [in Russian], Nauka, Moscow (1966).
S. A. Mazanik, Lyapunov Transformations of Linear Differential Systems [in Russian], BGU, Minsk (2008)
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Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 30, Part I, pp. 161–170, 2014.
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Zalygina, V.I. Lyapunov Equivalence of Systems with Unbounded Coefficients. J Math Sci 210, 210–216 (2015). https://doi.org/10.1007/s10958-015-2558-3
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DOI: https://doi.org/10.1007/s10958-015-2558-3