Dear T. Duvernet,
Buying rental property is a rent controlled area depends on the rules for the area. L.A. for instance I believe exempts single family homes and propertyt built since 1978. If it is vacant when you buy you can charge what the market will bear. After that you are limited by their rules. If you charge market rent and raise rents as much and as often as you can you may not be at any disadvantage versus non- rent controll.
Some cities (Santa Monica?) force landlords to comply with their limits EVEN IF THE UNIT IS VACANT WHEN YOU BUY! In other words you inherit the previous owner's last rent as a starting point as if there had been no vacancy. There are usually exceptions for evicting a tenant because you or a family member want to move in but you probably would need to pay your tenant and their cost to move.
If you have more questions contact me at 310 265 1816 or jim@BlackHorseRealty.biz. I have owned and managed rental properties in the South Bay since 1976.