Charles has just put out a great video (triggered by some comments from Jack Dorsey about the relative merits of Proof of Work) that explains Proof of Stake and some of the design decisions that fed in Ouroboros, the protocol that underpins the Cardano network.
Detailed, but if you want a technical analysis this is it…
Charles mentions a few papers in the video which we link for convenience:
The Bitcoin Backbone Protocol: Analysis and Applications, Juan A. Garay Texas A&M University [email protected], Aggelos Kiayias†‡ University of Edinburgh, IOHK [email protected], Nikos Leonardos†§, National and Kapodistrian University of Athens. [email protected], August 14, 2020
Ouroboros: A Provably Secure Proof-of-Stake Blockchain Protocol, Aggelos Kiayias∗ Alexander Russell† Bernardo David‡ Roman Oliynykov§ July 20, 2019