Linear-matrix-inequality observer design of nonlinear systems with unknown input and measurement noise reconstruction

We investigate the unknown-input observer design for a class of nonlinear systems with both unknown inputs and measurement noise. First, based on the techniques of linear matrix inequality and generalized systems, the original nonlinear system is transformed into an augmented generalized system, and a robust sliding-mode observer which can estimate both the states and measurement noise vector of the original system is developed. Second, a robust sliding-mode differentiator is considered to exactly estimate the derivative of the output vector of the augmented generalized system, and a kind of unknown information reconstruction method which can be used to estimated unknown inputs of original system is proposed. The proposed method avoids using the derivative information of system output. Finally, a train system model is used to illustrate the effectiveness of the proposed methods which not only estimates the states of the original system, but also reconstructs the unknown input and measurement noise.