This article presents a new method of fault detection for the two-stage chemical reactor system. The process can be carried out effectively in the presence of the time-delay and the unknown inputs and the parameter uncertainties by using the observer-based method technique. In order to detect the actuator fault, a novel unknown input observer is employed as the residual generator. Multi-objective optimization techniques and a new performance index are adopted to ensure the robustness and sensitivity of the fault detection observer. Then the problem of fault detection is reduced to the problem of model matching. Furthermore, sufficient conditions are obtained to guarantee that the error system is asymptotically stable with an H ∞ performance by means of the Lyapunov function technique. Finally, a two-stage chemical system is borrowed to demonstrate the effectiveness of the obtained methods.