  This paper deals with the problem of robust fault estimation for the
Lipschitz nonlinear systems under the influence of sensor faults and actuator
faults. In the proposed methodology, a descriptor system is formulated by
augmenting sensor fault vectors with the states of the system. A novel fast
adaptive unknown input observer (FAUIO) structure is proposed for the
simultaneous estimation of both faults and states of a class of nonlinear
systems. A new LMI condition is established by utilizing the
$\mathcal{H}_\infty$ criterion to ensure the asymptotic convergence of the
estimation error of the developed observer. This derived LMI condition is
deduced by incorporating the reformulated Lipschitz property, a new variant of
Young inequality, and the well-known linear parameter varying (LPV) approach.
It is less conservative than the existing ones in the literature, and its
effectiveness is compared with the other proposed approaches. Further, the
proposed observer methodology is extended for the disturbance-affected
nonlinear system for the purpose of the reconstruction of states and faults
with optimal noise attenuation. Later on, both designed approaches are
validated through an application of a single-link robotic arm manipulator in
MATLAB Simulink.
