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In this paper, we analyze the stability robustness of teleoperation systems, coupled to operators and environments with finite range of dynamic variations. A new graphical extension of the scattering-based absolute stability method  is proposed, which incorporates minimum inherent damping of the operator as well as bounds on the environment impedance. The proposed method provides both mathematical and visual aid for the determination of passive or active environment regions that result in coupled stability. Our rigorous studies have shown that for potentially unstable systems, as the operator minimum damping grows, the environment stability region grows to include all passive environments.