For Lipschitz nonlinear descriptor systems with bounded input disturbances, by solving a Lyapunov equation, a robust state-space observer is proposed to simultaneously estimate descriptor system states, actuator faults, their finite times derivatives, and attenuate input disturbances in any desired accuracy. The considered faults can be unbounded (provided that their qth derivatives are bounded), the present fault estimation approaches can handle a large class of faults. By using the estimates of descriptor states and faults, and the linear matrix inequality (LMI) technique, a fault-tolerant control scheme is worked out. The nonlinear fault-tolerant control system can be made solvable, causal, asymptotically stable, and attenuate input uncertainties in terms of the prescribed performance index. Only original coefficient matrices are used in the proposed state-space observers and fault-tolerant controllers; therefore, the present design approaches are preferable in applications. Finally, a numerical example is given to illustrate the design procedure and simulations demonstrate the efficiency of the proposed design.