This study examines the performance of a nonlinear sliding mode controller in cooperative control of the intelligent connected vehicles systems. The study begins by proposing a vehicle-to-vehicle car-following model that takes into account the impacts of disturbances both external and within in the system. Subsequently, an adaptive exponential reaching sliding mode controller based on a non-singular terminal sliding mode variable is proposed. It is analyzed theoretically using Lyapunov method, differential method and difference method and the results show that using the new controller, the system can converge in finite time with enhance dynamic performance. Finally, to verify the effectiveness of the controller proposed in this study, numerical experiments in MATLAB and simulation experiments in the ROS-Gazebo environment are conducted, and the results show that the controller proposed in this study enables the intelligent vehicle system to maintain stable operation in the face of interferences. Experiment results are in accordance with theoretical analysis.