It seems intuitive to me that, in a digital system, a system sampling the error rate "too slowly" will fail to stabilize the system.
Is there a theory/set of metrics/equation I can use to represent this in the frequency or time domain?
i.e.
$$ e(t) : \text{Actual error (not sampled error) with respect to time} \\ e(s) : \text{Laplace or frequency domain representation of error signal} \\ F_s : \text{Rate at which error is sampled} $$
If $e(t)$ has frequency components much higher than $F_s$ (or maybe if $F_s < 2\text{max}[e(s)]$ ), is it possible to properly control the system?