Robust integral-observer-based fault estimation for Lipschitz nonlinear systems with time-varying uncertainties

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.