There's been a number of attempts at least, see Ouroboros: https://eprint.iacr.org/2016/889.pdf https://eprint.iacr.org/2016/889.pdf I'm still on the fence abo

There's been a number of attempts at least, see Ouroboros: https://eprint.iacr.org/2016/889.pdf https://eprint.iacr.org/2016/889.pdf I'm still on the fence about the viability of PoS from the perspective that PoW at least means you have a chance of reward from using mining hardware that you probably already own, whereas PoS increases that barrier of adoption.