California kind of has it state wide. Rent increases are capped at 5% + CPI up to 5% annually. Which means it’s 5-10% annually depending on that years inflation. If you don’t increase one year, you can’t increase double the next year. The downside is this means a lot of places just automatically do the 5% increase every year and then there are also issues with people being evicted for “renovations” so that they can increase the rent more than the cap for new tenants.

It’s better than no protections but it’s still not great.