  In data-driven control, a central question is how to handle noisy data. In
this work, we consider the problem of designing a stabilizing controller for an
unknown linear system using only a finite set of noisy data collected from the
system. For this problem, many recent works have considered a disturbance model
based on energy-type bounds. Here, we consider an alternative more natural
model where the disturbance obeys instantaneous bounds. In this case, the
existing approaches, which would convert instantaneous bounds into energy-type
bounds, can be overly conservative. In contrast, without any conversion step,
simple arguments based on the S-procedure lead to a very effective controller
design through a convex program. Specifically, the feasible set of the latter
design problem is always larger, and the set of system matrices consistent with
data is always smaller and decreases significantly with the number of data
points. These findings and some computational aspects are examined in a number
of numerical examples.
