Abstarct: In this thesis, we study observer-baxsed fault detection and isolation problem for Multiple input-Multiple output. After presenting some definitions, we introduce model-baxsed fault detection considering summary of different generating residual methods. Then, we introduce briefly observer-baxsed method and finally, we survey and compare two adaptive observer-baxsed fault detection methods. In the main method, we evaluate the effects of Hurwitz matrix in Lyapunov matrix equation and the constant coefficient in adaptive observer on residual signal in fault detection and isolation system. Here we use a method of actuator fault detection which is baxsed on a bank of adaptive observer and several bank for actuator fault isolation. The linear unmanned aircraft system Machan have been examined. In this method we use the system model outputs and adaptive observers outputs to generate residuals. The results show fast detection and isolation time without false alarm.