CONTROLLABILITY OF INVARIANT CONTROL SYSTEMS AT UNIFORM TIME
Let G be a compact and connected semisimple Lie group and E 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 SE such that the system turns out controllable at uniform time s(Sigma). 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 = boolean AND(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(3), where 3 is the Lie algebra determined by the control vectors.
compact semisimple uniform-time reverse-system