This paper addresses the controller design problem for bilateral teleoperation over unreliable networks. The stability and tracking performance analysis are presented for a novel force-reflecting emulator control scheme. The performance (stability, synchronization, transparency) is guaranteed by Hinf control theory and delay-scheduled Lyapunov-Krasovskii functionals (LKF), which could improve the existing stability criterion. The design is achieved by using Linear Matrix Inequality (LMI) optimization. For the simulation, firstly, numerical examples are given to demonstrate the effectiveness and benefits of the delay-scheduled LKF-based stability results; secondly, the proposed controller design solution is illustrated by various simulations and compared with other recent approaches under different working conditions, e.g. abrupt tracking motion and wall contact.