Bobby Brown -- NEW ADDITION ... Wife Gives Birth to Daughter

Finally some good news for Bobby Brown -- his wife gave birth to a bouncing baby girl Saturday ... at the same hospital where Kim Kardashian had North!

Alicia Etheredge was admitted to Cedars Sinai hospital on Friday -- and was induced on Saturday. It's the couple's 2nd child together ... and Bobby's 6th child overall.

It's a bright spot for Brown ... whose daughter with Whitney Houston, Bobbi Kristina, is still in bad shape in hospice care in Atlanta ... where she's been since the end of June.

Bobby Brown has been trying to return to normalcy since B.K. was found unconscious in a bathtub back in January ... and recently performed a concert in Atlanta ... but he's clearly having a tough time.