  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.
