Active disturbance rejection control approach to stabilization of lower triangular systems with uncertainty

In this paper, we apply the active disturbance rejection control (ADRC) to stabilization for lower triangular nonlinear systems with large uncertainties. We first design an extended state observer (ESO) to estimate the state and the uncertainty, in real time, simultaneously. The constant gain and the time-varying gain are used in ESO design separately. The uncertainty is then compensated in the feedback loop. The practical stability for the closed-loop system with constant gain ESO and the asymptotic stability with time-varying gain ESO are proven. The constant gain ESO can deal with larger class of nonlinear systems but causes the peaking value near the initial stage that can be reduced significantly by time-varying gain ESO. The nature of estimation/cancelation makes the ADRC very different from high-gain control where the high gain is used in both observer and feedback. Copyright (C) 2015 John Wiley & Sons, Ltd.