Plausible = something that could happen. The word is very similar to "possible," but implies that something is a correct assumption.

"The Earth being round is a plausible idea."

Convincing = something that makes people think its real/true (but it may not be in reality).

"His suit and tie costume makes him a very convicing president."

Persuasive = used when someone is trying to get someone else to do something they want/agree with them. It is also used as a roundabout way to convey something that is sexual.

"He is a successful businessman mostly because of his persuasive personality. Everyone he meets with ends up on his side."

"He is being fired mostly because of his persuasive attitude. No one in the office feels comfortable when he is around."

Persuasive and convincing are very similar but persuasive, I believe, is usually attributed to people. Convincing is attributed to anything.

Hope that helps!

PLAUSIBLE seeming reasonable or probable. "a plausible explanation". synonyms: credible, reasonable, believable, likely, feasible, tenable, possible, conceivable, imaginable. CONVINCING capable of causing someone to believe that something is true or real. "there is no convincing evidence that advertising influences total alcohol consumption" synonyms: cogent, persuasive, plausible, powerful, potent, strong, forceful, compelling, irresistible, telling, conclusive "a convincing argument" (of a victory or a winner) leaving no margin of doubt; clear. PERSUASIVE Good at persuading someone to do or believe something through reasoning or the use of temptation. "an informative and persuasive speech" synonyms: convincing, cogent, compelling, potent, forceful, powerful, impactful, eloquent, impressive, influential, sound, valid, strong, effective. There are subtle differences between the three and they may not always be interchangeable.