Would it be:
Having studied late at night, he slept.
Or something else?
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Studying late at night, he slept
does not make any sense because the actions were not concurrent.
Having studied late at night, he slept
is grammatical, but not common. In English, we tend not to rely solely on tense to specify sequence. So more common would be
After studying, he slept.
The sequence is specified without any need for a perfect construction.