Stability Analysis of Linear Active Disturbance Rejection Control

In this paper, we study the stability problem of second-order linear active disturbance rejection control of second-order linear systems without external disturbances. The state space model of the closed-loop system is established through two subsystems, state feedback and linear extended state observer error, and the convergence of the closed-loop system is analyzed with the help of the characteristic equations of the state space model. When the system internal disturbance is known, the stability condition for the closed-loop subsystem is obtained as long as the derivative of the system disturbance satisfies the Lipschitz condition. When the system internal disturbance is not considered and the system internal disturbance is unknown, two methods of Nyquist stability criterion and Lyapunov function are applied respectively, and the system is asymptotically stabilized over a large range by theoretical analysis and mathematical proof, and the simulation results verify the effectiveness of the proposed method.