What is the Past participle form of word stay up?

The phrase "stay up" doesn't have a past participle form. "Stay up" is a phrasal verb, meaning it's a verb plus a preposition or adverb. Phrasal verbs don't usually form past participles in the same way that regular verbs do.

To express the past tense of "stay up", you would use the past tense form: stayed up.

For example:

* Present: I stay up late every night.

* Past: I stayed up late last night.