Kybernetika

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. Precisely, to find a positive time s_Σ such that the system turns out controllable at uniform time s_Σ. 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 = \bigcap_{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.