It’s a strange feeling to have somebody shoot at you. (Michael Swan, Practical English Usage)
In the above sentence, does “to have” means “to persuade”?
It means that you get somebody to shoot at you by asking or ordering them to do it.
to cause something to happen or someone to do something:
If you wait, I’ll have someone collect it for you.
I think Torsten is incorrect here. The sentence means “It’s a strange feeling when someone is shooting at you.” Here, the “have” does not mean you have asked or persuaded someone to shoot at you. It is closer to “It’s a strange feeling to have purple hair.” or “It’s a strange feeling to have your uncle as your biology teacher.”
So to suffer and/or experience:
have verb (SUFFER)
B1 [ T + past participle ] to suffer something that someone does to you:
She had her car stolen (= it was stolen) last week.
Thesaurus: synonyms and related words
have verb (EXPERIENCE)
A2 [ T ] to experience something:
We’re having a wonderful time here in Venice.
We didn’t have any difficulty/problem finding the house.
Actually, that what I had written initially :-). What about ‘It’s a strange feeling to have somebody shooting at you’?
In that case and also with the infinitive the meaning is linked to experiencing something. This is different from the idea of having something done to you.