In Continuous system, the Laplace transform for a pure delay is just:
The delay occurred in the forward or feedback path, the transfert function ,specifically, in the frequency domain, the bode diagramme will be the same for both. e.g.
When the time delay is small, the feedback system can be kept stability.
However, the system will become instable by increasing the delay. In the meantime, the delay also degrades the system response time and control precision.
Once the random delay to a certain extent, the stability of the system is difficult to guarantee.