This is convolvulus sabatius, one of the best groundcovers I have found for this area. Its common name is Gound Morning Glory, but don't let the name scare you, it is not invasive.
It does form a thick mat that is covered with purplish-blue flowers almost year round, which makes the need for weeding unnecessary where it is planted. It is fairly drought tolerant once it is established. I use is a lot around the feet of roses and although it takes awhile to get going, once it makes itself at home it will fill in and spread nicely.