This paper addresses the estimation problem of states and their derivatives for the Time Delay Control (TDC), a robust control technique for nonlinear systems. To this end, an observer design method is presented. Then, in simulations, the controller/observer has been applied to a nonlinear plant, with satisfactory results. Finally, experiments were undertaken on a DC servo motor subject to substantial inertia variations and external disturbances. The results showed that the controller/observer performs quite robustly under those variations and disturbances, and is much less sensitive to sensor noise than the controller using numerical differentiations.