If you're looking for articles on Persuasion, what you're really looking for is literary criticism. Literary criticism is any "evaluation, analysis, description, or interpretation of literary works" (Leon, "Literary Criticism"). Sometimes literary criticism can be found on the Internet, but it is often difficult to find. The best place to search for any type of literary criticism is in a library, particularly a college or university library.
A few articles of literary criticism can be found on eNotes. Articles by Brian Southam and Gary Kelly both analyze the characterization of the Elliot family. The articles can also be found in the book Novels for Students, in a chapter titled "Critical Essays on Persuasion," by Wendy Perkins. Another article titled "Rationality and Rebellion: Persuasion and the Model Girl" by Mary Waldron can be found in Jane Austen and the Fiction of Her Time. Waldron counteracts the popular critique that Anne Elliot is far too perfect a character and instead points out that she has human flaws. Another article by Alistair M. Duckworth, titled "Austen's Accommodations" and found in Critical Essays on Jane Austen, also analyzes what Austen is saying about wealth and stature through Anne's rejection of marrying to acquire an estate in favor of marrying a man she loves who has a fortune, but no estate.