  A common assumption on the deployment of safeguarding controllers on the
digital platform is that high sampling frequency translates to a small
violation of safety. This paper investigates and formalizes this assumption
through the lens of Input-to-State Safety. From this perspective, and
leveraging control barrier functions (CBFs), we propose an alternative solution
for maintaining safety of sample-and-hold controlled systems without any
violation to the original safe set. Our approach centers around modulating the
sampled control input in order to guarantee a more robust safety condition. We
analyze both the time-triggered and the event-triggered sample-and-hold
implementations, including the characterization of sampling frequency
requirements and trigger conditions. We demonstrate the effectiveness of our
approach in the context of adaptive cruise control through simulations.
