Controllability and synthesis of control for nonlinear systems

The problems of controllability of motion with feedback are solved when the equations of a system have linear approximation, at that by virtue the smallness of the nonlinear part and controllability of the linear approximation this property is preserved at the nonlinear perturbation. The problem is solved by Lyapunov functions method and comparison methods for a finite and infinite time. The results are illustrated on the example of the controllability for the simplest mechanical system.