The problem of fault estimation for nonlinear systems with Lipschitz nonlinearities is addressed in this work for the estimation of both the system fault and states. In the proposed approach disturbance is regarded to be a function which is nonlinear and coupled with states of the system, and fault to be a function which is additive. In order to diagnose the fault and reduce the disturbances effects by dissipativity theory, Luenberger and two unknown input observers (UIOs) are designed separately. If the system satisfies the matching condition, the first UIO can accurately estimate faults by decoupling the effects of state-coupled disturbances. Otherwise, the second UIO estimates faults by decoupling partial disturbances, and attenuating the disturbances which cannot be decoupled. The essential conditions for all designed observers to exist are stated. Finally, the suggested method is applied to a robot by simulation to analyse its performance.