Is there any series of games that were released on the PlayStation systems in order?

Not that I can recall. I do remember Digimon World 1-3 being on PS1, and the 4th installment being released on the Xbox though (which was awkward..). Then there's Medievil, there's a remake of the first game for the PSP. Other than that, not that I remember of. Sorry if this was slightly unrelated to your question, but this was all I coukd think of at the top of my head.

Oh, I think Persona 1 and 2 was for PS1. and Persona 2 was for PS2. Persona 3 and 4 was PS2 as well, I think.

Edited above ; Thanks, Wikipedia.