  Linear scalar differential equations with distributed delays appear in the
study of the local stability of nonlinear differential equations with feedback,
which are common in biology and physics. Negative feedback loops tend to
promote oscillation around steady states, and their stability depends on the
particular shape of the delay distribution. Since in applications the mean
delay is often the only reliable information available about the distribution,
it is desirable to find conditions for stability that are independent from the
shape of the distribution. We show here that the linear equation with
distributed delays is asymptotically stable if the associated differential
equation with a discrete delay of the same mean is asymptotically stable.
Therefore, distributed delays stabilize negative feedback loops.
