  This note analyzes incoherent feedforward loops in signal processing and
control. It studies the response properties of IFFL's to exponentially growing
inputs, both for a standard version of the IFFL and for a variation in which
the output variable has a positive self-feedback term. It also considers a
negative feedback configuration, using such a device as a controller. It
uncovers a somewhat surprising phenomenon in which stabilization is only
possible in disconnected regions of parameter space, as the controlled system's
growth rate is varied.
