"I woke up tired."
We have subject/(phrasal) verb/adjective.
So this looks like a linking verb with a predicate adjective. ("I am tired", "I became tired", "He seemed tired"). But since when is 'woke up' a linking verb? Is there a finite list of linking verbs or is it open? And I thought that a linking verb wasn't a 'doing' verb but 'woke up' seems like a 'doing' verb.
Note also that "I woke tired" or "I awoke tired" doesn't seem right. Why does the phrasal verb work but not the single word versions? Is it just usage?
And please don't say that 'tired' is an adverb because plainly it isn't, for any number of reasons--morphology being just the obvious one.