Can I divorce my incompetent husband?

Consider the Social Security angle if he earned substantially more than you did. Find a Certifified Elder Law Attorney, they have extra qualifications. nelf.org for a listing.
This is a complicated issue.

Only an elder law attorney can tell you. It would seem like you have a good chance of getting what you want because you have lived separate lives. On the other hand, if he dies before you, you may be denied the choice of receiving his Social Security benefits in lieu of yours if you want that option. Contact an attorney now.

I don't know much about this one, but all I can ask is whether or not any of the assets were in both names or just one. What does your agreement say? What's this agreement notarized and signed in front of witnesses or even a lawyer? As long as you have a prenup agreement that you both signed when he was competent, I don't see where there would be a problem as long as both of you agreed and it was actually placed on file

Your divorce will be easily granted due to prior separation. However, that does not protect you from Medicaid insisting that all assets be accounted for and fairly divided according to their rules. By divorcing him, you will have no rights to a community spouse allowance. Think it over with an attorney.

I don't know how medicaid sees a separation agreement, it could be complicated so you would do well to see an attorney who is well versed in medicaid and legal separations and not just a divorce attorney. I really don't expect an answer, but why didn't you just divorce in the first place?