Residents of just about every state use the usual English conventions to form the demonym
Hawaii - Hawaiian, Alaska - Alaskan, Kansas - Kansan, Florida - Floridian, Wisconsin - Wisconsinite, Rhode Island - Rhode Islander, Texas - Texan, until we come to Indiana.
Things were already confusing enough, so they're officially called Hoosiers, since "Indianian" would mean "of the land of the land of the people of India".
I only scanned it briefly, but I could not find Illinois on that page. I've lived in Illinois all my life, and I can't for the life of me figure out what we call ourselves!
Illinoisan just looks weird...but spellcheck seems to think it's a word, so let's just go with that. I usually just say, "I'm from Illinois."