Abstract: Fault estimation for linear systems based on a class of adaptive observers is investigated. The system states and faults can both be estimated by such adaptive observers. Utilizing the H∞ tracking performance, the design procedure and condition of stability of the adaptive observers are given. The fault estimation error is irrelevant to the magnitude of fault but relevant to the change rates of fault and H∞ tracking index. Therefore, the estimated fault can approximate to the real fault to any degree of accuracy. A simulation of sensor fault estimation is carried out for induction motor to verify the effectiveness of the proposed method.