Abstarct: In this thesis, a brief introduction of the various types of fault and the relevant theories has been illustrated. Then, the dynamic model of the inverted pendulum system has been described as a case study. In order to detect and isolate of fault in the mentioned system, sliding mode observer and fuzzy sliding mode observer baxsed on T-S model have been proposed. The Lyapunov stability analysis has been utilized to ensure the boundedness of the closed-loop system. Simulation results confirm the potential and effectiveness of the proposed FDI.