Reducible linear system

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of ordinary differential equations

A system


that can be transformed into a system with constant coefficients by a change of variables , where is a Lyapunov transformation. If the mapping is continuous and periodically depends on , then (*) is a reducible system (Lyapunov's theorem). The system (*) is reducible if and only if there is a Lyapunov transformation and an operator such that every solution of (*) has the form

(Erugin's criterion).


[1] A.M. Lyapunov, "Stability of motion" , Acad. Press (1966) (Translated from Russian)
[2] N.P. Erugin, "Reducible systems" Trudy Mat. Inst. Steklov. , 13 (1946) (In Russian)
How to Cite This Entry:
Reducible linear system. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by V.M. Millionshchikov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article