Geodesic
Lyapunov equivalence of systems with unbounded coefficients
Trudy Seminara im. I.G. Petrovskogo, Trudy Seminara imeni I. G. Petrovskogo, Tome 30 (2014) no. 30, pp. 161-170 
V. I. Zalygina. Lyapunov equivalence of systems with unbounded coefficients. Trudy Seminara im. I.G. Petrovskogo, Trudy Seminara imeni I. G. Petrovskogo, Tome 30 (2014) no. 30, pp. 161-170. http://geodesic.mathdoc.fr/item/TSP_2014_30_30_a7/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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.

[1] Bylov B. F., Vinograd R. E., Grobman D. M., Nemytskii V. V., Teoriya pokazatelei Lyapunova i ee prilozheniya k voprosam ustoichivosti, Nauka, M., 1966 | MR

[2] Mazanik S. A., Preobrazovaniya Lyapunova lineinykh differentsialnykh sistem, BGU, Minsk, 2008