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Coordinate transformation is applied to transform the system into a strict feedback system in normal form. The unknown non-linearity, parameter uncertainty and external disturbance are treated as an extended state of each subsystem, and a corresponding switched extended state observer (ESO) is designed. Based on the output of the switched ESO, a switching ADRC law is proposed. Rigorous proof is given to show that the switched ESO can estimate system states and the unknown non-linearity of each subsystem effectively. Furthermore, the proposed controller guarantees the closed-loop system be semi-globally uniformly ultimately bounded for a class of switching with average dwell time. 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