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This paper deals with the problem of robust fault estimation for theLipschitz nonlinear systems under the influence of sensor faults and actuatorfaults. In the proposed methodology, a descriptor system is formulated byaugmenting sensor fault vectors with the states of the system. A novel fastadaptive unknown input observer (FAUIO) structure is proposed for thesimultaneous estimation of both faults and states of a class of nonlinearsystems. A new LMI condition is established by utilizing the$\mathcal{H}_\infty$ criterion to ensure the asymptotic convergence of theestimation error of the developed observer. This derived LMI condition isdeduced by incorporating the reformulated Lipschitz property, a new variant ofYoung inequality, and the well-known linear parameter varying (LPV) approach.It is less conservative than the existing ones in the literature, and itseffectiveness is compared with the other proposed approaches. Further, theproposed observer methodology is extended for the disturbance-affectednonlinear system for the purpose of the reconstruction of states and faultswith optimal noise attenuation. Later on, both designed approaches arevalidated through an application of a single-link robotic arm manipulator inMATLAB Simulink.

Estimating the Faults/Attacks using a Fast Adaptive Unknown Input Observer: An Enhanced LMI Approach