The necessary and sufficient condition for the uncertain control gain in active disturbance rejection control

Considering the control problem for nonlinear uncertain systems, the tolerable range of uncertain control input gain is a fundamental issue. The paper presents the necessary and sufficient condition for the well-performed closed-loop system based on active disturbance rejection control (ADRC) design. Via the proposed necessary and sufficient condition, the maximum tolerable range of the uncertain control gain is quantitatively presented, which reveals the capability of ADRC to handle the uncertainties related with control input. Moreover, under the proposed necessary and sufficient condition, both the transient performance and the steady state property of the ADRC based closed-loop system are rigorously analyzed.