This paper addresses the problem of state estimation and sensor fault reconstruction conjointly for a class of nonlinear systems with time-varying uncertainties for which the nonlinear characteristic satisfies the Lipschitz circumstance. A hybrid approach based on an integral observer and sliding-mode theory has been proposed in order to model sensor fault as a virtual actuator one. For the augmented model, the observer matching condition is not satisfied. To overcome this problem, a new method, which improves the design approach and enhances the rapidity of the fault estimation convergence, has been proposed. The fault estimation error effect is minimized by integrating the H ∞ disturbance attenuation level. The proposed design is formulated and derived as a linear matrix inequality problem. Parameters of this observer are calculated through the linear matrix inequality technique. The proposed method has been validated through an example of a single-link manipulator robot. Simulation results show that this approach can estimate the state and the sensor fault successfully, despite the time-varying uncertainties and the presence of unknown inputs.

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This paper presents a robust fault diagnosis scheme for a class of uncertain nonlinear systems whose nonlinear function satisfies the Lipschitz condition with unmatched time-varying uncertainties, external disturbances and perturbed output. The design procedure combines the high robustness of the nonlinear unknown input observer with sliding-mode techniques in order to enhance the estimation qualities. The proposed design is derived and expressed as a linear matrix inequality optimization problem. Additionally, we have provided an approach to reduce conservatism in the derivation of the stability conditions. The effectiveness of this observer and the fault diagnosis scheme are shown by applying them to a single-link manipulator. Simulation results are presented to validate the proposed approach and show the robustness for the system nonlinearity and unmatched time-varying uncertainties.

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