Robust absolute stability analysis for interval nonlinear active disturbance rejection based control system

Active disturbance rejection control (ADRC) is a relatively new, quite different but very practical control technology, which shows much promise in replacement of proportion-integration-differentiation (PID) with unmistakable advantage in performance and practicality. This paper mainly concerns with the robust absolute stability of the ADRC based control system with parameter perturbations of the plant, i.e., ADRC based interval control system. Firstly, the system is transformed into a perturbed indirect Lurie system. Then, the Popov criterion and its robust version are presented and some new methods are developed to analyze the (robust) absolute stability for the interval control system. Furthermore, an example is presented to illustrate (robust) absolute stability analysis via the above methods, which verifies the convenience and practicability of these methods and shows the strong stability robustness of ADRC in the presence of parametric uncertainties.