New to Solar systems, would this work and is it a thing?

Hello,

I’m very new to solar systems and I was wondering if what I want is something that exists and works.

So basically, I moved to a new home, to which I’m planning to install a solar system with batteries, not to go off the grid, but to have energy in case of a power outage.

So I had kind of this idea but I’m not sure if it works;

Basically, my plan is to install solar panels and a system of 3 batteries. But the idea is to have the grid AND panels charge my batteries all the time and have the batteries deliver electricity to my house all the time.

Does this work? The reason I want to do this is also because the voltage isn’t very stable at times and I figured I could have stable voltage that way.

Thanks!