Vehicle platoons employing Cooperative Adaptive Cruise Control (CACC) exhibit outstanding performance. However, communication interruptions can destroy string stability and jeopardize driving safety of the platooning systems. To address this issue, this paper proposes a controller switching strategy and derives an analytical model to determine the boundary of communication delays. When the communication delay exceeds this theoretical boundary, the system seamlessly transitions from the primary CACC controller to a backup Adaptive Cruise Control (ACC) controller. The cost function and co-states are continuously adjusted during this transition using a Gaussian membership function. Analytical derivations demonstrate that the proposed switching strategy theoretically guarantees string stability. Comprehensive simulations further validate its effectiveness through both standardized scenario-based evaluations and real-world tests using the NGSIM dataset. Compared with existing methods, the proposed approach improves the string stability by 16.87% and enhances the safety index by 68.28%.