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Connected and automated vehicle platoons (CAVPs) are considered an effective way to alleviate traffic congestion, reduce the incidence of traffic accidents, and improve vehicle economy in the intelligent transportation system (ITS). Vehicles in the CAVPs can communicate with each other through V2X technology, which could optimize the economy of the platoon. Cooperative adaptive cruise control (CACC) can make effective use of the characteristics of CAVPs and contribute to resource conservation, ecological driving, and traffic system development. In this paper, a two-stage CACC method is proposed for CAVPs to reduce fuel consumption in the multislope road section. In the first stage, the optimal velocity profiles for the leader based on dynamic programming (DP) are planned according to the road information and the fuel consumption model. In the second stage, a vehicle longitudinal third-order differential dynamics model is utilized to build the platoon time-delay system considering communication delay and actuator delay. A feedback controller is developed for each vehicle considering the internal stability and the string stability of the CAVPs. Results show that the proposed method can save 5.33% of fuel consumption compared to the constant speed cooperative adaptive cruise control (CS-CACC) method and has a better tracking performance compared to the model predictive control (MPC) method. The CACC method proposed in this paper can provide a theoretical basis and data support for building an ecological CACC strategy for CAVPs. [ABSTRACT FROM AUTHOR]