I don't know what it is but it is a perennial I have seen them for years, especially along the side of the road, and I have quite a few in my back yard as well. If you just want to kill it roundup should do the trick.
@Paul M Doesn't round up contain Glyphosate? I would reccomend torching it if killing is the aim (depending on the area where Eulalia lives, of course)
As a beekeeper, I'm for responsible torching too. Many chemicals for home use contain high concentrations of neonicotinoids which also kill pollinators - bees, butterflies, etc.
Without being preachy, (it's just that I know that not everyone gardens,) without pollinators and pollination, many food source plants will not "fruit," thereby negatively impacting our food supply.
For anyone interested, I've included a link from the Xerces Society showing a list of products to avoid. (Cut and paste link in your browser) www.xerces.org/wings-magazine/neonicotinoids-in-your-garden
I think it is Sericea Lespedeza. It is sometimes used for hay or forage for farm animals. It is drought tolerant and will grow where other grasses won't.
It looks like milkweed to me...the Monarch butterflies need it to survive