Stability of active disturbance rejection control for uncertain systems: A Lyapunov perspective

In this work, we introduce a simple stability analysis to justify, under some suitable assumptions, the active disturbance rejection control method, used in the feedback regulation of a substantially uncertain plant. A criterion is obtained that allows us to define under what conditions closed-loop stability can be assured. When the plant is mostly unknown, the criterion allows us to guarantee exponential convergence for the output-feedback regulation problem, in the presence of a constant external perturbation, and practical stability when the external perturbation and the tracking reference signal are both time-varying. In the latter case, the confinement error can be made as small as desired. To carry out the corresponding stability analysis, we derive the tracking error equation, and the observation error equation. To decouple these error equations, we use the Sylvester equation. Finally, we applied the direct Lyapunov method to analyze the corresponding convergence of the observation error and of the tracking error.