Feedback information and actuation delays in Connected and Automated Vehicle (CAV) systems are detrimental to the string stability of CAV platoons. A generic approach is proposed to design platooning controllers that explicitly compensate for delays in communication, sensors and vehicle actuators and can be applied to platoons with different communication topology and different spacing policies. The main mechanism behind the delay-compensating design is to facilitate the host vehicle’s future status (thus compensating for actuation delay) to track the preceding vehicles’ history status (thus compensating for communication and sensing delays). This is realized by reformulating the desired spacing policies. Controller analysis shows the string stability of the proposed framework is guaranteed under delays from heterogeneous sources. Simulation is carried out to compare the string-stability performance of the designed systems with the baseline controllers without delay compensation. Simulation results verify that our approach generates controllers that require smaller time gap/spacing to keep the string stability of the systems than baseline controllers.