The problem of controlling synchronous motors, driven through AC/DC rectifiers and DC/AC inverters is addressed. The control objectives are three fold: (i) forcing the motor speed to track a varying reference signal in presence of motor parameter uncertainties;(ii) regulating the DC Link voltage; (iii )assuring a satisfactory power factor correction (PFC) with respect to the power supply net .First, a nonlinear model of the whole controlled system is developed in the Park-coordinates. Then, a robust nonlinear controller is synthesized using the damping function version of the back stepping design technique. A formal analysis based on Lyapunov stability and average theory is developed to describe the control system performances. Despite parameter uncertainties,all control objectives are proved to be asymptotically achieved up to unavoidable but small harmonic errors (ripples).