Remark 3: The interested readers are encouraged to refer to [29], [30] for the stability proof of the system (50).Remark 4: In this paper, the adaptive fuzzy approximation integrated with the disturbance observer is employed to reduce the magnitude of the gain ks(t). Therefore, the sliding gain ks(t) can be selected based on the bounded value rather than the original unknown component ((q; q_; )+), as shown in (22). Therefore, suppose that the estimated error is small, the chattering in this paper is almost eliminated since the adaptation gain ks(t) can be selected as a smaller value.