The stability of completely controllable systems

The subject of this paper is the stability of completely controllable systems defined on a smooth manifold. It is known that the controllability sets of symmetric systems generate singular foliations. In the case when the controllability sets have the same dimension, a regular foliation arises. Thus, the possibility of applying the methods of foliation theory to control theory problems arises. This paper presents some of the authors' results on the possibility of applying the theorems on the stability of leaves to the problems on the stability of completely controllable systems and on the geometry of attainability sets. Smoothness throughout the work will mean smoothness of class $C^{\infty}$.