These are the mages I'd consider to be "control" mages:
There are a couple I'm not sure on but I decided not to include: 
To me a control mage can be simply defined as a mage who has the ability to exercise a large amount of control over a fight, typically for extended periods. This can be done primarily via zone control and crowd control, usually a solid mixture of both. While yes, a lot of the champions I'm listed are also very clearly in the burst mage category ( and in particular), this is mostly because mages tend to do a variety of things and it's possible to combine burst with control elements.
The most similar mage to in terms of how she controls fights is probably - both of them create zones where enemies don't want to be (Anivia ult, Azir soldier location), both of them force suboptimal pathing on enemies (Anivia W, Azir ult) and both of them output a potentially severe amount of crowd control (Anivia Q/R, Azir ult, Q + Rylai's soldiers). However, obviously they do things quite differently in other ways with Azir having units to micro-manage and Anivia... not having to do that, so liking Anivia doesn't mean you'd like Azir. You should try your hand at all of the mages I listed, but Azir, Syndra and Ori are all difficult to pick up (not that Anivia is easy) so be prepared to put time into learning them. The only people I don't enjoy much in the list myself are Azir and Lux.
