Controllability and synthesis of control for nonlinear systems

We solve motion control problems with feedback under the linear approximation of equations of the considered system. Due to the smallness of the nonlinear part and the controllability of the linear approximating system this property is preserved under a nonlinear perturbation. We perform the study by the method of Lyapunov functions and by the comparison method within finite and infinite time intervals. We illustrate the obtained results by an example of controlling a simple mechanical system.