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A class of single output nonlinear systems with an uncertain parameter is considered. A diffeomorphism is first introduced to simplify the system structure, then, by employing an adaptive approach to identify the unknown parameter, a sliding mode approximate estimator is developed to estimate the system state variables. Based on the estimator, a fault estimation scheme is proposed together with an approach to optimise the estimation error using linear matrix inequality techniques. A simulation example is given to demonstrate the proposed scheme.