# Reducible linear system

From Encyclopedia of Mathematics

*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).

#### References

[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: http://encyclopediaofmath.org/index.php?title=Reducible_linear_system&oldid=18924

This article was adapted from an original article by V.M. Millionshchikov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article