Abstract

Let G be a compact and connected semisimple Lie group and Σ an invariant control systems on G. Our aim in this work is to give a new proof of Theorem 1 proved by Jurdjevic and Sussmann in [6]. Precisely, to find a positive time SΣ such that the system turns out controllable at uniform time SΣ. Our proof is different, elementary and the main argument comes directly from the definition of semisimple Lie group. The uniform time is not arbitrary. Finally, if A = ∪t>0 A(t, e) denotes the reachable set from arbitrary uniform time, we conjecture that it is possible to determine A as the intersection of the isotropy groups of orbits of G-representations which contains exp(Z), where Z is the Lie algebra determined by the control vectors.