By using various sensors to measure the surroundings and sharing local sensor information with the surrounding vehicles through wireless networks, connected and automated vehicles (CAVs) are expected to increase safety, efficiency, and capacity of our transportation systems. However, the increasing usage of sensors has also increased the vulnerability of CAVs to sensor faults and adversarial attacks. Anomalous sensor values resulting from malicious cyberattacks or faulty sensors may cause severe consequences or even fatalities. In this paper, we increase the resilience of CAVs to faults and attacks by using multiple sensors for measuring the same physical variable to create redundancy. We exploit this redundancy and propose a sensor fusion algorithm for providing a robust estimate of the correct sensor information with bounded errors independent of the attack signals, and for attack detection and isolation. The proposed sensor fusion framework is applicable to a large class of security-critical Cyber-Physical Systems (CPSs). To minimize the performance degradation resulting from the usage of estimation for control, we provide an $H_{infty}$ controller for CACC-equipped CAVs capable of stabilizing the closed-loop dynamics of each vehicle in the platoon while reducing the joint effect of estimation errors and communication channel noise on the tracking performance and string behavior of the vehicle platoon. Numerical examples are presented to illustrate the effectiveness of our methods.