Observer design and detection for nonlinear descriptor systems

A nonlinear observer is considered for a class of continuous nonlinear descriptor systems subject to unknown inputs and faults. This class is partly characterized by globally Lipschitz nonlinearities, and a member system may be singular and possibly non-causal. The observer structure chosen makes it useful for both state estimation for feedback controls and residual generation for fault detection. Results on the existence of solutions are given and some useful bounds are derived which are important in the observer design, which is based on a transformed system and on the solution of a Riccati equation. The existence, convergence properties and robustness of the observer are investigated by the use of a quadratic Lyapunov function. Conditions are given for a bound to hold on the norm of the transfer function relating the residual error to the disturbance (linear case). A design algorithm is given and applied to the estimation of the states of a flexible joint robot.