Convergence and stability analysis of active disturbance rejection control for first-order nonlinear dynamic systems

To quantitatively investigate the correlation between parameters, disturbance and stability of the linear active disturbance rejection control (LADRC) technique, this paper provides a perspective of first-order nonlinear dynamic systems, and obtains the stable region of LADRC and reduced-order LADRC according to the Lyapunov function and the Markus-Yamabe theorem, along with mathematical proofs for global stability and asymptotic regulation. To be specific, regardless of whether plant dynamics are exactly known or unknown, the control bandwidth can be chosen arbitrarily from the obtained feasible region as long as the derivative of the disturbance satisfies a Lipschitz condition, or some knowledge of the boundary is available. Moreover, simulations are presented to testify the reliability of the results for different disturbances that are probably known or unknown when designing the extended state observer. The results show the validity and feasibility of this analysis.