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A sliding-mode controller with an integral-operation switching surface is adopted to control the position of an induction servo motor drive. Moreover, to relax the requirement for the bound of uncertainties, a fuzzy neural network (FNN) sliding-mode controller is investigated, in winch the FNN is utilised to estimate the bound of uncertainties real-time. The theoretical analyses for the proposed FNN sliding-mode controller are described in detail. In addition, to guarantee the convergence of tracking error, analytical methods based on a discrete-type Lyapunov function are proposed to determine the varied learning rates of the FNN. Simulation and experimental results show that the proposed FNN sliding-mode controller provides high-performance dynamic characteristics and is robust with regard to plant parameter variations and external load disturbance. Furthermore, comparing with the sliding-mode controller, smaller control effort results, and the chattering phenomenon is much reduced by the proposed FNN sliding-mode controller.