High Gain Observers with Multiple Sliding Mode For State and Unknown Input Estimations

High-gain observers with multiple sliding modes for simultaneous state and unknown input estimations of a class of MIMO nonlinear systems are systematically developed in this paper. The unknown inputs are assumed to be bounded and not necessarily Lipschitz, and do not require any matching condition. A new nonlinear transformation is proposed and the observer design and analysis are performed in the transformed domain. By imposing a structural assumption on the unknown input distribution matrix, the observability of the unknown inputs w.r.t. the outputs is safeguarded. In the multiple sliding mode, the disturbances/unknown inputs under the equivalent controls becomes the increments of the Lipschitzian functions, and the convergence of the estimation error dynamics can be proven similar to the analysis of a high-gain observer. Also, the unknown inputs can be reconstructed from the multiple sliding modes structurally. The observer in the original space is readily obtained by means of inverse transformation. Finally, simulation results are given to demonstrate the effectiveness of the proposed method.