Sunset's Western Garden Book
contains lists of plants (trees, shrubs, ground covers, bulbs) suitable to special conditions. In my edition (which is the 7th; the current ed. is the 8th), the list of ground covers suitable for "Dry Areas" lists 25 species.
Twenty (yes, 20!
) of these ground covers are also listed as suitable for full sun!
However, they're specified by Sunset climate zones. Los Angeles County, and even the City of Los Angeles, contain several Sunset climate zones. Zones 22, 23, and 24 cover most of the L.A. Basin, but Zones 18 through 21 are also represented. Rainfall is one of the determinants of Sunset climate zones, and a ground cover will most likely be heavily dependent on rainfall for its survival. (I'm imagining that it would be very difficult, if not impossible, to hand-water or establish an irrigation system on such a steep hillside.)
Take a look at the Sunset book, maybe at your local library, gardening center, or hardware store, and ascertain your Sunset climate zone. Then select a few of the ground covers for Dry Areas which you like. Consult with a nursery on the planting density (how will you plant these? is the hillside too steep to dig in plants? do you need to broadcast seeds and hope for the best? etc.), and look towards planting in late October or early November--just ahead of the first expected seasonal rains.
Sunset Zone 17, USDA Zone 9