In order to quickly drive to the target lane, traditional human-driving vehicles(HVs) often forcibly change to the target lane, which is deemed as traditional human-driving vehicles cut-in maneuvers. However, this process will affect the stability of a mixed vehicle group composed of traditional human-driving vehicles and connected automated vehicles(CAVs) in the target lane. When a vehicle group consisting of multiple traditional human-driving in a lane cut-ins to the mixed vehicle group in the target lane, it will have greater impact on the stability of the mixed vehicle group. In response to this concern, the paper first characterizes the vehicle dynamics model to describe the smoothness of vehicle driving and the stability of the mixed vehicle group. Then, to guarantee the stability of a vehicle group composed of multiple traditional human-driving vehicles cut-ins to a mixed vehicle group, this paper proposeds a mixed vehicle group cooperative control method via considering communication delay and reaction delay based on consensus constraints and communication topologies from the perspective of cyber-physical systems(CPS). Simultaneously, the Lyapunov-Krasovskiis theory is used to further analyze the stability conditions of the proposed control method. Finally, the results from the simulation experiments show the effectiveness and feasibility of the proposed control method.