This paper investigates the problem of state and actuator/sensor fault (ASF) estimation for nonlinear systems described by Takagi-Sugeno (T-S) fuzzy models subject to external disturbances. A robust adaptive observer (RAO) is designed to estimate the system state, sensor faults and actuator faults conjointly. For the convergence analysis of all estimation errors, a fuzzy Lyapunov functional candidate combined by free weighting matrices have been constructed to obtain more relaxed results. The design conditions, taking into account the H-infinity performance, are formulated in terms of Linear Matrix Inequalities (LMIs). Finally, a comparative study is presented to prove the superiority of the proposed method.