  Prescribed-time algorithms based on time-varying gains may have remarkable
properties, such as regulation in a user-prescribed finite time that is the
same for every nonzero initial condition and that holds even under matched
disturbances. However, at the same time, such algorithms are known to lack
robustness to measurement noise. This note shows that the lack of robustness of
a class of prescribed-time algorithms is of an extreme form. Specifically, we
show the existence of arbitrarily small measurement noises causing considerable
deviations, divergence, and other detrimental consequences. We also discuss
some drawbacks and trade-offs of existing workarounds as motivation for further
analysis.
