  According to recent results, convergence in a prespecified or prescribed
finite time can be achieved under extreme model uncertainty if control is
applied continuously over time. This paper shows that this extreme amount of
uncertainty cannot be tolerated under sampling, not even if sampling could
become infinitely frequent as the deadline is approached, unless the sampling
strategy were designed according to the growth of the control action.
Robustness under model uncertainty is analyzed and the amount of uncertainty
that can be tolerated under sampling is quantified in order to formulate the
least restrictive prescribed-time control problem that is practically
implementable. Some solutions to this problem are given for a scalar system.
Moreover, either under a-priori knowledge of bounds for initial conditions, or
if the strategy can be selected after the first measurement becomes available,
it is shown that the real, practically achievable objectives can also be
reached with linear time-invariant control and uniform sampling. These
derivations serve to yield insight into the real advantages that implementation
of prescribed-time controllers may have.
