A nonlinear observer is considered for a class of discrete nonlinear d
escriptor systems subject to unknown inputs and faults. This class is
partly characterized by globally Lipschitz nonlinearities, and a membe
r system may be singular and possibly non-causal. The structure propos
ed for the observer makes it useful for both state estimation for feed
back controls and residual generation for fault detection. Results on
the existence of solutions are given and some useful bounds are derive
d which are important in the observer design. The proposed nonlinear o
bserver is based on a transformed system and on the solution of a Ricc
ati equation. The existence, convergence proper ties and robustness of
the observer are investigated by the use of a quadratic Lyapunov func
tion. A design algorithm is given and applied to the estimation of the
states of a flexible joint robot.