The observer-based fault detection method, which is robust, strong, high efficiency and good reliability, has been a hot in the model-based fault diagnosis method. The mathematical model of the system was made full use of by the observer-based fault detection method. But the H_∞optimization technology was used in most of the observer-based fault detection systems, which was proved to be complex and inconvenient in engineering practice.The open-loop and closed-loop fault systems are introduced to explain how to model for the fault systems on the basis of introducing the observer-based fault diagnosis principle. The models of the inverted pendulum control system, the three tank system and the vehicle lateral dynamic system are analyzed minutely.For LTI discrete systems, combining the observer theory with the parity space, the evaluation function is established, and the threshold is confirmed. The traditional optimization problems are transformed into the design of the observer and filter, which are simplified, so the good results are obtained. Numerical simulation shows the effectiveness of the method.Finally, for LTI continuous system, the output observer is constructed to generate the residual. Curbing the disagreeable aspect and strengthening the needed aspect of the residual by adding a post-filter, which are aim to distinguish the influence of the fault and the model uncertainty, and the algorithm is simple. The detecting result of using post-filter is proved to be better than the detecting result of non post-filter by numerical simulations and the simulations of the inverted pendulum control system, the three tank system and the vehicle lateral dynamic system. Simulation examples show the effectiveness of the design method and the algorithm.