This groundcover plant (sometimes called blue eyes) looks very similar to Convolvulus sabatius, which grows in many Sydney gardens. Evolvulus pilosus belongs to the same plant family (Convolvulaceae) but comes from the North American prairies. It has simple leaves with a silvery tone and rounded bright blue flowers for a long period from summer to autumn. It grows well in hot, dry positions and appears to be very tough. It can be used to tumble over the sides of retaining walls or hanging baskets, as well as a groundcover. It can be propagated by cuttings taken in spring or autumn. There are various named forms, including 'Blue Eyes'.
Postscript: my plant eventually faded away and I am now growing Convolvulus sabatius again instead. Possibly my soil was too heavy for the Evolvulus or the position not hot and dry enough.
Flowers in January, February, March.