Stuff like Nyquist criterion just sort of appears out of nowhere as functions.
I guess the big one is feedback being the magic, and then the complex plane tells you where that blows up.
Black's canonical 1934 paper[1] Stabilized Feedback Amplifiers, which had an outsized influence on EE classical control theory, may have something to do with that:
Results of experiments, however, seemed to indicate something more was involved and these matters were described to Mr. H. Nyquist, who developed a more general criterion for freedom from instability applicable to an amplifier having linear positive constants.
...which directly cites Nyquist's canonical 1932 paper[2] Regeneration Theory.
Techniques often need very strong assumptions about the systems being modeled, which severely limits their usefulness.
In fact, CT is sort of the antitheses of the currently most hyped way of modeling systems: Machine Learning.
Also systems modeling is not the same as control theory. You could indeed utilize machine learning to model a system, which you could then control by classical controllers. On the other hand, control algorithms that use machine learning are a thing.
Perhaps just a coincidental namespace collision: Process ID, not Proportional-Integral-Derivative.