In this paper, a safe control strategy is considered in the situation when a platoon of vehicles need to decelerate rapidly. When the vehicles ate spaced closely, it is known that the reference information should be transmitted to the whole platoon to minimize the undesirable effects of small leader disturbances. However, the vehicle control should also depend on the preceding vehicle position to maintain the desired distance. Tracking the preceding vehicle position can lead to amplification of the control input along the following vehicles, therefore the vehicles in the rearward generally exert larger maximum control input than the vehicles in the front. The theoretical bounds for the $i^{th}$ vehicle control input are calculated using a linear vehicle and controller model. In the simple illustrative example, the designed controller maintains string stability, and the control inputs of the following vehicles stay within bounds.