Abstract˖A robust H ∞ control method based on linear matrix inequality (LMI) is proposed for force feedback space teleoperation systems with large time-varying delays and the uncertainty of the environment model parameters. This method only needs to know the bounds of the delay interval for teleoperation systems with unknown and variable round trip time delays. It also can solve the problem that the parameters of the environment are uncertain and obtain good position and force tracking

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... ces. The master and slave dynamics are respectively transformed to state space equations, and they are incorporated to a uniform form, which is discretized in succession. A state-feedback controller is designed for the whole systems based on LMI method; the stability of the closed-loop system is analyzed by defining a Lyapunov function; and sufficient conditions for the controller are presented which enable the closed-loop system to be asymptotic stability as well as guarantee a prescribed position tracking performance under the cases that the parameters of the environment are certain or uncertain. Simulation results demonstrate that the proposed method enables the teleoperation system not only asymptotic stability, but also taking on good position and force tracking performances.