It is taught, mostly in graduate school control theory courses which are typically found in ece departments. Typically called "linear systems" as a starter course, there is not really a standard textbook as it can be taught as pure math or as a more applied subject. For nonlinear systems, which deals more with theoretical things such as existence of solutions, the textbook by khalil is pretty standard. I'm pretty sure there are some decent YouTube lecture series on state space control. They should discuss controllability/observability, some basic feedback schemes, etc. Oddly, a lot of control theory is more concerned with examining systems than with actually developing controllers... Most modern work in control theory is state space as opposed to classical frequency response methods as it handles multiple input multiple output systems much better.