Yeah, it's not raising, it's control, as zompist said. Though it's not as simple as deletion, I think.
Supposedly you've got something like this:
Mary persuaded John [John to leave]
And then you delete the second John because it corefers with the object of the matrix clause.
That makes it seem like you could have something like this:
Mary persuaded John [Fred to dance]
And then you wouldn't delete "Fred," because it doesn't corefer with "John" The problem is, of course, that the result isn't grammatical. I don't think the issue is just semantic (maybe John has authority over Fred's dancing behaviour).
With "persuade," in English, I'm pretty sure(*) the embedded subject has to corefer with the matrix object. So the rule here can't just be that you delete the embedded subject whenever it happens to corefer with the matrix object. So this is "obligatory control."
In some languages there's another possibility, topic drop. If you're free to drop topics, then you'll often get embedded clauses with no overt subject, but this won't really be about control, it'll just be topic drp. (Or pro drop, which I guess would work the same in these contexts.)
That's actually an issue that arises with Dixon's analysis of Dyirbal. Control is one of the issues people look at when thinking about syntactic ergativity: in most languages, even ones that have other syntactically ergative patterns, only the subject of an embedded clause can be controlled. Dixon argued that Dyirbal is an exception to this, and allows control of absolutive arguments generally, but apparently Dyirbal allows topic drop and there's some question of what's really going on here. (Citation: Aissen,
Dyirbal ergativity. She also argues against Dixon's conclusions about coordination structures. I don't have an opinion about either topic.)
(*NOTE.) Does anyone thing something like "Mary persuaded John Fred to be fired" could be ok? (If so, would it entail that Mary persuaded John to fire Fred, or could it be someone else who's to do the firing?)
Edit. Oh, and similar issues come up in arguments about whether Pirahã has recursion, since a control structure would be recursive but a topic-drop one maybe wouldn't have to be. For example:
https://ling.auf.net/lingbuzz/004928