This paper presents a cooperative control method for connected and automated vehicle (CAV) platooning, thus specifically addressing the challenge of sensor measurement errors that can disrupt the stability of the CAV platoon. Initially, the state-space equation of the CAV platooning system was formulated, thereby taking into account the measurement error of onboard sensors. The superposition effect of the sensor measurement errors was statistically analyzed, thereby elucidating its impact on cooperative control in CAV platooning. Subsequently, the application of a Kalman filter was proposed as a means to mitigate the adverse effects of measurement errors. Additionally, the CAV formation control problem was transformed into an optimal control decision problem by introducing an optimal control decision strategy that does not impose pure state variable inequality constraints. The proposed method was evaluated through simulation experiments utilizing real vehicle trajectory data from the Next Generation Simulation (NGSIM). The results demonstrate that the method presented in this study effectively mitigates the influence of measurement errors, thereby enabling coordinated vehicle-following behavior, achieving smooth acceleration and deceleration throughout the platoon, and eliminating traffic oscillations. Overall, the proposed method ensures the stability and comfort of the CAV platooning formation.