The design of unknown input observer based on unknown input and measurement noise compensation

This paper considers the problem of unknown input observer design for a class of nonlinear Lipschitz systems with both unknown input and measurement noise. First, the estimations of measurement noise and the analytical solution of unknown input are provided, and then they are introduced into the observer design as compensation to make them decoupled from the system. Second, an observer which is able to provide the estimates of the system states, unknown inputs and measurement noises are developed based on linear matrix inequity (LMI). Third, in order to avoid using the differential information of output when the unknown inputs are reconstructed, a series of second-order sliding mode observers are considered to offer the exact estimates of the output derivatives in a finite time. Finally, a numerical simulation example is given to show the effectiveness of the proposed method.