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In this paper, a set based approach is presented for safety verification and performance analysis of automated driving systems. As an example, reachability analysis technique is used to study the minimum required safe inter-vehicle distance for two given adaptive cruise controllers, a state feedback and a state feedback/feedforward controller designed based on mixed d H2/3 control. Not surprisingly, the results indicate that a shorter inter-vehicle distance can be achieved when a feedforward term used in the controller. In addition, we show how backward reachability analysis and invariant set theory can be used to find the Maximal Admissible Safe Set. This is defined as the set of position error, relative speeds and acceleration, which a given controller is guaranteed to control to the desired speed and inter-vehicle distance, while fulfilling vehicle physical constraints and avoiding rear-end collisions with the preceding vehicle. The calculation of the Maximal Admissible Safe Set is demonstrated for the two aforementioned controllers. Furthermore, the presented verification method is extended to account for the case of vehicle model with polytopic uncertainties and delay. The results on the reachability analysis are verified experimentally using an emergency braking scenario.