The platoon of connected autonomous vehicles plays an essential role in future intelligent transportation. It can improve traffic efficiency and release traffic congestion. However, there are lots of existing challenging problems of the control of connected autonomous vehicles, such as the negative impact caused by wireless communication and disturbance. To solve these challenges, a multi-objective asymmetric sliding mode control strategy is proposed in this paper. Firstly, the asymmetric degree is introduced in the topological matrix. Then, a sliding mode controller is designed targeting platoon's tracking performance. Moreover, Lyapunov analysis are used via Riccati inequality to find the controller's gains and guarantee internal stability and Input-to-output string stability. Finally, a non-dominated sorting genetic algorithm is utilized to find the Pareto optimal asymmetric degree regarding the overall performance of the platoon, including tracking index, fuel consumption, and acceleration standard deviation. Four different information flow topologies, including a random topology are studied. The results indicate that the proposed asymmetric sliding mode controller can ensure platoon's stability while improving its performance. The tracking ability is improved by 54.61% and 75.17%, fuel economy is improved by 0.78% and 6.34% under the Urban Road and Highway Case Study, respectively.