On convergence of the discrete-time nonlinear extended state observer

This paper concerns with the convergence of the discrete-time nonlinear extended state observer (ESO). Several kinds of discrete-time nonlinear ESO (NLESO) are proposed and then sufficient conditions based on linear matrix inequality (LMI) method are obtained to quantitatively reveal the relationship between the plant, the sampling interval, the parameter values of NLESO and its convergence. The theoretical results are verified by simulation using a motion control system. It shows that there may exist an optimal ω_o for a certain fixed sampling interval, and a smaller sampling interval generally generates better performance. What's more, the proposed digital implementations of NLESO improve its performance over traditional Euler approximation discretization method.