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The master-slave control design problem is considered for the networked teleoperation system with friction and external disturbances. A new finite-time synchronization control method is proposed with the help of adaptive fuzzy approximation. We develop a new nonsingular fast terminal sliding mode (NFTSM) to provide faster convergence and higher precision than the linear hyperplane-sliding mode and the classic terminal-sliding mode (TSM). Then, the adaptive fuzzy-logic system is employed to approximate the system uncertainties, and the corresponding adaptive fuzzy NFTSM controller is designed. By constructing Lyapunov function, the stability and finite-time synchronization performance are proved with the new controller in the presence of system uncertainties and external disturbances. Compared with the traditional teleoperation design method, the new control scheme achieves better transient-state …