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The recent advancement in vehicular networking technology provides novel solutions for designing intelligent and sustainable vehicle motion controllers. This work addresses a car-following task, where the feedback linearisation method is combined with a robust model predictive control (RMPC) scheme to safely, optimally and efficiently control a connected electric vehicle. In particular, the nonlinear dynamics are linearised through a feedback linearisation method to maintain an efficient computational speed and to guarantee global optimality. At the same time, the inevitable model mismatch is dealt with by the RMPC design. The control objective of the RMPC is to optimise the electric energy efficiency of the ego vehicle with consideration of a bounded model mismatch disturbance subject to satisfaction of physical and safety constraints. Numerical results first verify the validity and robustness through a comparison between the proposed RMPC and a nominal MPC. Further investigation into the performance of the proposed method reveals a higher energy efficiency and passenger comfort level as compared to a recently proposed benchmark method using the space-domain modelling approach.