Creating new stable periodic orbit by small region feedback control

In this paper an important problem in chaos control theory concerningthe possibility of generating a new stable periodic solutionby a small feedback control law for a dynamical system is addressed.It is proved that a solution with an initial point being somekind of non-wandering property can become a new asymptoticallystable solution by a small feedback control law. This showsthat the popular opinion that a small control law is not ableto create a new periodic point is untrue, and suggests a newapproach to controlling chaos.