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At beginning, the dynamic model of QUAV at low speed including translational and rotational motions is derived by Newton-Euler formulation. Four control inputs generated by four rotors are employed to accomplish the up-down, translation, roll, pitch and yaw motions. In this total, the proposed system produces six outputs that will affect the trajectory and pose of a QUAV: its 3D position and angular position with respect to the world-fixed coordinate. Based on the data of input-output, two scaling factors are first used to normalize each sliding surface and its derivative. According to the concept of if-then rule, an appropriate rule table for the ith subsystem is obtained. Then the output scaling factor based on Lyapunov stability is determined. The purpose of using the proposed fuzzy decentralized sliding-mode under-actuated trajectory-tracking control (FDSMUTC) is the huge uncertainties of a QUIAV often caused by different flight conditions. Finally, the simulation example is applied to illustrate the corresponding procedure of controller design.