Stability of completely controllable systems

In this work, we discuss the stability of completely controllable systems defined on smooth manifolds. It is known that the controllability sets of symmetric systems generate singular foliations. In the case where the controllability sets have the same dimension, regular foliation arise. Thus, we can apply the methods of foliation theory to problems in control theory. In this paper, we present some results on the possibility of applying theorems on the stability of layers to the problem on the stability of completely controllable systems.