digital feedback stability
This is a sample and hold mixer where the output is the difference phase, frequency.
What is not shown is the fout is converted to a very narrow pulse which results in a DC voltage when in sync. The gain is proportional to the input signal so it is linear mixer.
The BW of the system with phase lead compensation for PID parameters determined the capture range of this PLL as well as the signal input and its SNR are details to improve this simple model.