The improvement of direct human–robot physical interaction has recently become one of the strongest motivation factors in robotics research. Impedance/admittance control methods are key technologies in several directions of advanced robotics such as dexterous manipulation, haptics and telemanipulation. In this paper, we propose a control scheme and a design technique for stabilising shared impedance/admittance-based bilateral telemanipulation under varying time delay. The proposed scheme introduces delay-adaptive non-linear damping to stabilise the impedance model. A modified version of the tensor product model transformation is applied to determine the tensor product type polytopic linear parameter varying (LPV) representation of the impedance controlled interaction model, such that the value of the actual time delay becomes an external parameter rather than an inherent property of the system. The main benefit of the proposed approach is that the model form it produces is amenable to the immediate application of modern, linear matrix inequality (LMI)-based multi-objective synthesis methods. The viability of the proposed methodology is demonstrated through a single DoF force reflecting tele-grasping application. The results are also confirmed through laboratory experiments which help to further highlight the perspectives of this novel approach.