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The control design problem is investigated for network-based teleoperation systems under the condition of asymmetric and time-varying delays. The classic teleoperation model is considered for which the position of the master is transmitted to the slave site as the control command and the slave torque is directly transmitted to the master in order for the user to have a feeling of the remote interaction. The slave controller is constructed based on the master-slave position error plus a new nonlinear damping function, while the master controller is composed of the transmitted slave torque and the introduced nonlinear damping function. By employing a new Lyapunov Krasovskii functional, we prove the exponential input-to-state stability of the closed-loop system. The relationship is built among the control design parameters and the maximum allowable time delays, which is in the form of linear matrix inequality. Both the simulations and experiments are performed to show the effectiveness of the proposed method. Compared with existing approaches, transmission delays considered are both time varying and asymmetric, and the passivity conditions on the remote environment and the human operator are removed. In addition, the method is very simple.