Learn Grammar| English Grammar : Modal auxiliaries : Could, Should, Might, Must, Ought to + have + Verb 3 | 1. Could + have + Verb 3
This Modals are used to express the real thing can be done in the past.
He could have done his homework
This implies that he will not do his homework last night.
He could have invited them.
Modals are often used in conditional sentences, especially type II.