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O. Perron (1930)
Über eine MatrixtransformationMathematische Zeitschrift, 32
A.M. Lyapunov (1956)
Sobr. soch. T. 2
ISSN 0012-2661, Differential Equations, 2007, Vol. 43, No. 12, pp. 1632–1637. c Pleiades Publishing, Ltd., 2007. Original Russian Text c E.A. Barabanov, 2007, published in Differentsial’nye Uravneniya, 2007, Vol. 43, No. 12, pp. 1592–1596. ORDINARY DIFFERENTIAL EQUATIONS Generalization of the Bylov Reducibility Theorem and Some Applications E. A. Barabanov Institute for Mathematics, National Academy of Sciences, Minsk, Belarus Received August 20, 2007 DOI: 10.1134/S0012266107120026 Consider the system of linear differential equations x ˙ = A(t)x, x ∈ R,t ≥ 0, (1) where n ∈ N is fixed and the coefficient matrix A(·):[0, +∞) → End R is piecewise continuous and uniformly bounded on the time half-line t ≥ 0. We denote the class of all such systems (1) by M , identify system (1) with its coefficient matrix, and write A ∈ M . By performing a linear n n nondegenerate (for all t ≥ 0) change of variables x = L(t)y with a continuous piecewise differentiable matrix L(·) in system (1), we obtain the system n −1 −1 y˙ = B(t)y, y ∈ R ,t ≥ 0, where B(t)= −L (t)L(t)+ L (t)A(t)L(t). (2) ˙ ˙ [Since L(·) is piecewise continuous, to be definite, we define
Differential Equations – Springer Journals
Published: Mar 25, 2007
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