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

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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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     author = {V. I. Zalygina},
     title = {Lyapunov equivalence of systems with unbounded coefficients},
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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/