Controllability of linear systems on non-abelian compact lie groups

Abstract

In this paper, we shall deal with a linear control system ? defined on a Lie group G with Lie algebra L(G). We prove that, if G is a compact connected Lie group, then the vector fields associated to dynamic of ? are conservative, and that if G is also non-Abelian then, by using Poincare Theorem, ? is transitive if and only if it is controllable.