The mechanics of power are complex and easily misunderstood. Modern English vocabulary on the subject does not help; it is often imprecise and equivocal (e.g. the word influence), lumps together different types of power (e.g. authority), and frequently conflates power and morality (e.g.
"My half-brother's code-key ring is not yours to trade," said Fell coldly.
"Oh, yes it is," said Mark. "I won it. I control it. I can destroy it. And"—he licked his lips; the girl raised the teacup again—"I paid for it. You would not now be offered this exclusive—and it is still exclusive—opportunity if not for me."
from Bujold, Lois McMaster. Mirror Dance (Vorkosigan Saga) (Miles Vorsokigan Book 8) . Kindle Edition.
The "I can destroy it" more or less sums up imperium I think. But he is enumerating the four words there. He has legitimacy to speak for it through "winning it" and also "paying for it". He has control, which I interpret as a combination of potestas and dignitas.
As for auctoritas? Fell is basically a space pirate, so there's an inherent problem there. But he does acknowledge Mark's power after this speech by offering for the ring, so he does have some recognition of the concept.