Learning models in control theory (adaptive control) are usually based on transfer function representations. In one way or another, these are about locating the unknown poles and zeroes of a transfer function on the complex plane. Optimal estimation and filtration problems are also done on the complex plane.

The connections between learning models in control theory and AI are quite close in some ways, but are kinda lost in history (back when control theory used to be called "analog computing.")

You won't find any of this stuff in AI machine learning textbooks. The reason is that control theory is founded upon the basic problem of stabilizing unstable systems. Stability problems naturally lead to differential equations and complex-plane methods. Learning problems are built on top of this foundation. You have to deal with learning and instability at the same time (dual control). This is never the case in machine learning, to my knowledge.

Most machine learning problems don't involve dynamics at all, or if they do, they are naturally stable and discrete-time dynamics, not things like trying to stabilize an airplane or spacecraft with unknown mass, structural damage etc.

So basically, if you add dynamics and stability issues to your learning problem (mostly the case with physical systems and real-time control), you'll probably run into complex analysis. If you're scanning credit card transactions for fraud, chances are, you won't (though in a weak sense, any time you deal with matrices, eigenvalues, singular values etc., you are inching close to complex analysis territory).