I don't recall much about control theory from university, but the one thing that did stick was state-space representation.
The part that got me was that you could take this arbitrarily-complex LTI system and basically turn it into a matrix that encapsulates everything. Any given state the system could exist in becomes a simple vector. Lots of crazy compositional techniques exist once you get your problems into this kind of shape.
Similarly, I like how any LTI system is just poles and zeroes in the s-plane. Or, if your system is sampled (DSP, and actually most signals you'll deal with in a computer), in the z-plane.
But not just every LTI system, ever sampled signal is poles and zeroes in the z-plane.
I have used that fact for years, and it still blows me away from time to time. Laplace and z-transforms are pretty magical, more so than Fourier even (which is basically a special case).
The part that got me was that you could take this arbitrarily-complex LTI system and basically turn it into a matrix that encapsulates everything. Any given state the system could exist in becomes a simple vector. Lots of crazy compositional techniques exist once you get your problems into this kind of shape.