Sliding-mode Observers for Nonlinear Systems with Unknown Inputs and Measurement Noise

This paper deals with the design of observers for Lipschitz nonlinear systems with not only unknown inputs but also measurement noise when the observer matching condition is not satisfied. First, an augmented vector is introduced to construct an augmented system, and an auxiliary output vector is constructed such that the observer matching condition is satisfied and then a high-gain sliding mode observer is considered to get the exact estimates of both the auxiliary outputs and their derivatives in a finite time. Second, for nonlinear system with both unknown inputs and measurement noise, an adaptive robust sliding mode observer is developed to asymptotically estimate the system's states, and then an unknown input and measurement noise reconstruction method is proposed. Finally, a numerical simulation example is given to illustrate the effectiveness of the proposed methods.