State estimation with unknown input and measurement disturbance reconstruction based on descriptor systems

The paper considers the problems of state estimation, unknown input and measurement disturbance reconstruction for a class of Lipschitz nonlinear system. By taking the measurement disturbance vector as an extended state vector, the original system is transformed into an augmented descriptor system. For the descriptor system, the necessary and sufficient condition of the existence of the unknown input observer is discussed first. Second, an adaptive and robust sliding mode observer which can estimate the states and the measurement disturbance of original system simultaneously is developed. Third, a second-order high gain sliding mode observer is used to exactly estimate the derivatives of the system outputs in a finite time. By using the estimates of the states and the output derivatives, a kind of algebraic unknown input reconstruction method is proposed. Finally, a simulation example to a modified single-link flexible joint robot is given to illustrate the effectiveness of the proposed method.