In this thesis, the investigation of asymptotic stability of the series DC motor with unknown load-torque and unknown armature inductance is considered. The control technique of recursive, or backstepping, design is employed. Three cases are considered. In the first case, the system is assumed to be perfectly known. In the second case, the load torque is assumed to be unknown and a proportional-integral controller is developed to compensate for this unknown quantity. In the final case, it is assumed that two system parameters, load torque and armature inductance, are not known exactly, but vary from expected nominal values within a specified range. A robust control is designed to handle this case. The Lyapunov stability criterion is applied in all three cases to prove the stability of the system under the developed control. The results are then verified through the use of computer simulation.