In this study, a novel fuzzy robust fault estimation scheme is developed for a class of nonlinear systems when both fault and disturbance are considered. The proposed scheme includes component fault with a nonlinear distribution matrix; as a result, the Takagi–Sugeno model is used to create multiple models. While the Takagi–Sugeno model is used for only the nonlinear distribution matrix of the fault signal, a larger category of nonlinear systems will be considered. This paper presents the problem of robust fault estimation based on fuzzy nonlinear observers, the first one is a fuzzy unknown input observer and the other one is a fuzzy sliding mode observer. The approach decoupled the faulty subsystem from the rest of the system through a series of transformations. Then, the objective is to design a fuzzy unknown input observer guaranteeing the asymptotic stability of the error dynamic using the Lyapunov method and completely removing disturbances; meanwhile, a fuzzy sliding mode observer is designed for a faulty subsystem to generate an estimation of fault based on a quadratic Lyapunov function and some matrices inequality convexification techniques. The sliding motion affects only the faulty subsystem through a novel reduced order fuzzy sliding mode observer; meanwhile, all disturbances are completely removed by fuzzy unknown input observer. Sufficient conditions are established in order to guarantee the convergence of the state estimation error and the results are formulated in the form of linear matrix inequalities. Thus, an exact fault estimator is determined on the basis of linear matrix inequality conditions while the estimation fault is completely insensitive to the disturbance. Finally, a simulation study on an electromagnetic suspension system is presented to demonstrate the g performance of the results compared with a pure sliding mode observer.
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