This paper presents an integrated platoon control framework for heterogeneous vehicles on curved roads with varying slopes, aerodynamic drag, and wireless communication delays. First, a linear heterogeneous vehicle platoon model with decoupled longitudinal and lateral dynamics is built based on nonlinear feedback linearization and arc-length parametric transformation of an arbitrary curved road. The external disturbances are also considered, including the up-down road slopes, wind and equivalent time-delays caused by the wireless communication delay and discrete data in onboard sensors. Second, to achieve stable platoon control on a curved road, the platoon uses the state-feedback control method in the longitudinal direction while each vehicle tracks the centerline of the curved road to realize lateral control. Longitudinally, an $ H_\infty$ platoon controller is designed based on the Lyapunov-Krasovskii functional to ensure the inner-vehicle and string stability of the platoon, which suffers from parameter uncertainty, and external disturbances. Additionally, the $ \mathcal {L}_2$ string stability is defined to guarantee that the perturbations do not grow unbounded as they propagate through the platoon. Simulation results indicate that the proposed robust controller achieves proper platoon intervehicle spacing in both the longitudinal and lateral directions.