The problems of traffic congestion, car accident and fuel scarcity can be relieved by forming vehicular platoon with small inter-vehicle spacing, where vehicles transmit their position, velocity and acceleration profiles via wireless communication networks. However, unavoidable and heterogeneous communication delays in reality among vehicles become a challenging problem in controller design process. This study presents a decoupled control method for a vehicular platoon with heterogeneous communication delays and sampled data, which are closer to the real world. Directed graphs are adopted to describe the information flow of connecting automated vehicles. By designing the state estimator, the influence of communication delays that bring the state errors can be eliminated. The complex coupled platoon control system is decoupled through the eigenvalue decomposition of information topology and the linear transformation of the whole system. Based on this almost decoupled system, linear matrix inequalities (LMIs) are derived to numerically acquire the distributed feedback controller of every vehicle. Furthermore, by using the monotonicity of construction function, the number of original multiple LMIs are converted to only two, which contain both the minimum and maximum eigenvalues of the communication topology matrix. The solving process is greatly simplified. The stability performance of the whole platoon system is theoretically analyzed by constructing Lyapunov function, containing the linear quadratic function of states. Also, the performance of asymptotic stability and anti-disturbance ability are measured by H-infinity norm. Simulations are carried out to demonstrate the effectiveness of the proposed control method. The results show that the decoupled control strategy can maintain the stability of the whole platoon system with heterogeneous communication delays. Moreover, stability performance can be ensured under different communication topologies.