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A class of nonlinear systems that are output-input stable in healthy situation is considered. An observer-based fault-tolerant control (FTC) method is proposed to make the origin asymptotically stable in spite of faults. The proposed FTC method can help to construct a family of Lyapunov functions for a class of switched nonlinear systems with unfixed or fixed dwell periods and to design a switching law that guarantees the fault-tolerant asymptotic stability of the origin. Several examples are included to illustrate the design procedures.