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The paper is concerned with the task of robust adaptive fault estimation and an unknown input decoupling for nonlinear systems using a quadratic boundedness approach. In particular, the fault estimation strategy and decoupling of the unknown input is based on an unknown input observer. The above methods are used to describe a robust fault and state observer problem by a set of linear matrix inequalities, which are efficiently handled by freely available solvers. The proposed approach allows obtaining a feasible set of joint state and fault estimation errors. Based on this knowledge, the confidence intervals of the system state and actuator fault, which supports diagnostic decisions, are proposed. The final part of the paper presents an illustrative example concerning an aerodynamical twin-rotor system, which exhibits the performance of the proposed approach.

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