The problem of fault estimation and fault tolerant control for Lipschitz nonlinear systems subject to actuator and sensor faults is investigated in this paper. A fault decomposition technique is introduced to design a set of iterative estimation observers for the system in consideration. The obtained mean sequence of estimates, under certain conditions, converge to the true values of state and multi-faults. A convergence theory with a theoretical proof is given. A sufficient LMIbased stability condition dependent on the coefficient matrix of disturbance is proposed to determined the observer gains. Finally, an output feedback FTC is designed to stabilize the Lipschitz nonlinear system. The longitudinal dynamics of an aircraft is applied to test the proposed method.