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This paper focuses on enhancing lateral motion stability in an independent drive electric vehicle (IDEV) under various uncertainties such as parameter variations, external disturbances, and input time delay. Initially, a new mathematical model for the IDEV is developed, accounting for these uncertainties. Further, a sliding mode predictive control (SMPC) utilizing an adaptive reaching law (ARL) is designed to alleviate the chattering effects, expedite reaching time and mitigate the impact of input time delay. Additionally, two virtual control signals are generated to improve tracking accuracy. An optimal control allocation technique is then introduced to map virtual control signals to actual control inputs. To further enhance control robustness and path-tracking accuracy, disturbance observer and delay estimator are designed to accurately estimate unknown disturbances and input time delay, with feedback incorporated into the SMPC. Simulation and hardware-in-the-loop (HIL) experiments are performed for two specific driving maneuvers and the results demonstrate the effectiveness of the proposed ARL-SMPC design.