State and unknown input estimations for a special class of nonlinear uncertain systems

In this paper, we develop a robust high gain observer for state and unknown input estimations for a special class of single-output nonlinear systems. The unknown input is characterized by a scalar disturbance that is distributed by a known nonlinear vector. Ensuring the observability of the disturbance with respect to the output, the disturbance can be estimated from the sliding surface. Under a Lipschitz condition for the nonlinear part, the high gain observers are designed under some regularity assumptions. In the sliding mode, the convergence of the estimation error dynamics is proven similar to the analysis of high-gain observers. The proposed observer can be applied for fault detection and isolation problems.