Do they bloom with a yellow head? Sorta look like goldenrod.

While a natural vegetation is always best for steep slopes, have you considered a mulch mat? There is a nonwoven mat made from industrial hemp that is all natural, easy to install, and nice looking. Because it's a mat that is anchored down, it won't slide down the hill. It'll slowly biodegrade over time. Combining it with some plantings would be a cost effective solution; over time, as the mats degrade, the vegetation can take over. Like any mulch product, though, you have to like the looks of it. Here's the website: www.woven-earth.com. Outside of the mulch, I'd agree with morpheuspa that a wildflower mix would walk the lines between aesthetics, effectiveness, and labor.

Yes, I recognize this is an old post, but for the benefit of others landing on this page... I'm 99% sure this is Creeping Beggarweed or Spanish Clover (D. incanum/D. laxiflorum). Mine produce a deep pink, almost purple flower. I spent an exhaustive afternoon in my back yard digging a ~6' x 6' patch of it out of my St. Augustine about 2 yrs. ago. I would compare the underground root system to that of Torpedo grass... invasive and virtually impossible to eradicate. My temporary joy of digging out the mother lode tap root (at least 10" deep!) was quashed when sprigs of it started popping up again. As the natural/organic method failed, I got some Roundup. The grass has almost fully recovered now; I get an occasional sprig though. Then I noticed it was invading a stretch of front yard near the street. Mother Nature sent Irma to help me with that area. Put the debris pile on top of it and by the time it was picked up, mostly everything was dead underneath. It made it easy to pull most of the roots out then. So for the sprigs that have survived both there and in back, I take a can with both ends cut off, slip the weed inside of it (Beggarweed and/or Torpedo), and try to protect the surrounding St. Augustine as I spray the Roundup. My condolences to anyone battling this... good luck!

It could be quack grass.