Asian Journal of Mathematics

Volume 23 (2019)

Number 4

High order linear extended state observer and error analysis of active disturbance rejection control

Pages: 631 – 650



Ji Shi (Department of Mathematical Sciences, Tsinghua University, Beijing, China)

Xiuqiong Chen (Yau Mathematical Sciences Center, Tsinghua University, Beijing, China)

Stephen S.-T. Yau (Department of Mathematical Sciences, Tsinghua University, Beijing, China)


In this paper, we aim to give a delicate analysis of the error dynamics of linear active disturbance rejection control (LADRC) for nonlinear time-varying plants with unknown dynamics. We first give precise upper bounds for the estimation error of linear extended state observer (LESO) and tracing error and then generalize the results to a higher order LADRC. The settling time is studied numerically. The results can be very useful for determining the parameters of LADRC. The results are very effective as verified by various simulations.


active disturbance rejection control, feedback linearization, output feedback and observers, stability of nonlinear systems, uncertain systems

2010 Mathematics Subject Classification

65L20, 65L70, 93C10, 93D15, 93D20

This work is supported by the National Natural Science Foundation of China under Grant [11471184] and by the start-up fund from Tsinghua University.

Received 11 November 2017

Accepted 21 May 2018

Published 7 January 2020