On stability and robustness of linear active disturbance rejection control: A small gain theorem approach

Small gain theorem is used to interpret stability and robustness of linear active disturbance rejection control(LADRC). For the case linear unmodeled dynamic and additive external disturbance, LADRC system is decomposed into two interconnected subsystems. The first subsystem includes all parametric uncertainty of the plant, while the second has a gain which can be adjusted by choosing the parameters of LADRC. If the product of the two subsytems' gains is less than one, then LADRC is stabilizing and robust against parametric variant. Furthermore, tuning observer bandwidth is interpreted as an approach to adjust the second subsystem's gain when the parameters of the plant is unknown. And it is proved that when the observer bandwidth is large enough, the second subsystem's gain is small enough so that LADRC is stabilizing.