There are no references to my knowledge on global controllability of non linear systems except algorithmic approach for this problem in finite state systems (which is NP hard). But you may look into Vidyasagar's book for affine case also see Nijmeijer and Van der Craft. Most results of non linear systems are local in nature. Affne systems seem to simplify the problem for which the rank criterion of controllability distribution gives a condition. But even this is not easy to numerically compute since that involves global solution to non linear equations. Hope this helps.

Thank you. I will first find the references you that you have mentioned.

i THINK THIS TYPE IS NOT YET AVAILABLE

First you present system is called - a linear time-dependent system.

For this class of systems I have met the results based on the symmetry group.

Look in this area. Really, I only known publications in Russian. If you really need to - I find and translate.

Yes. If it possible send it to me

KRISHCHENKO A.P.

Reference

There's quite a formal description in a mathematical form.

Russian word I think is easy to understand with the help of Google translator.

Here is a list of references in English

Thank you for the references ...

I encounter some difficulties in the exploitation of  the attached documents. Is it possible to have more precise (english) references? Thank you all.