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Safety is the foremost concern for autonomous platooning. The vehicle-to-vehicle (V2V) communication delay and the sudden appearance of obstacles will trigger the safety of the intended functionality (SOTIF) issues for autonomous platooning. This research proposes a holistic robust motion controller framework (MCF) for an intelligent and connected vehicle platoon system. The MCF utilizes a hierarchical structure to resolve the longitudinal string stability and the lateral control problem under the complex driving environment and time-varying communication delay. Firstly, the H-infinity feedback controller is developed to ensure the robustness of the platoon under time-varying communication delay in the upper-level coordination layer (UCL). The output from UCL will be delivered to the lower-level motion-planning layer (LML) as reference signals. Secondly, the model predictive control (MPC) algorithm is implemented in the LML to achieve multi-objective control, which comprehensively considers the reference signals, the artificial potential field, and multiple vehicle dynamics constraints. Furthermore, three critical scenarios are co-simulated for case studies, including platooning under time-varying communication delay, merging, and obstacle avoidance scenarios. The simulation results indicate that, compared with single-structure MPC, the proposed MCF can offer a better suppression on position error propagation, and get improvements on maximum position error in the three scenarios by $19.2\%$, $59.8\%$, and $15.3\%$, respectively. Last, the practicability and effectiveness of the proposed MCF are verified via hardware-in-the-loop experiment. The average conducting time of the proposed method on Speedgoat real-time target machine is 1.1 milliseconds, which meets the real-time requirements.