  We consider the stability and performance of a discrete-time control loop
used as a dynamic nuller in the presence of a relatively large time delay in
its feedback path.
  Controllers of this form occur in mm-wave telescopes using
frequency-multiplexed Transition Edge Sensor (TES) bolometers. In this
application, negative feedback is needed to linearize a Superconducting Quantum
Interference Device (SQUID) used as an amplifier. $M$ such feedback loops are
frequency-multiplexed through a SQUID at distinct narrowband frequencies in the
MHz region. Loop latencies stem from the use of polyphase filter bank (PFB) up-
and down-converters and have grown significantly as the detector count in these
experiments increases.
  As expected, latency places constraints on the overall gain $K$ for which the
loop is stable. However, latency also creates spectral peaks at stable gains in
the spectral response of the closed loop. Near these peaks, the feedback loop
amplifies (rather than suppresses) input signals at its summing junction,
rendering it unsuitable for nulling over a range of stable gains.
  We establish a critical gain $K_C$ above which this amplifying or
"anti-nulling" behaviour emerges, and find that $K_C$ is approximately a factor
of 3.8 below the gain at which the system becomes unstable.
  Finally, we describe an alteration to the loop tuning algorithm that selects
an appropriate (stable, effective for nulling) loop gain without sensitivity to
variations in analog gains due to component tolerances.
