I am calling this centipede grass. It was in an area of a neglected yard. It was a couple of feet tall & entangling the existing plantings. We mowed the area down then sprayed it with glycosphate. It is brown now & we would like to eventually use the area as a vegetable garden, utilizing lasagne method. The question is do the remnants need to be uprooted or can we do the lasagne layering over the remnants?
It is probably Bermudagrass, which is horribly aggressive. You can pinpoint your weedy grass in our Weed gallery. Here is the Bermudagrass page: http://extension.umd.edu/hgic/bermudagrass
Glyphosate is the best way to get rid of this grass, but let the area stand for a while so that any living bits have time to re-emerge and you can hit them again. Be sure you get all of it before you plant. Totally dead plant material can be allowed to naturally decompose. Just be sure it is totally dead.
One caution, most glyphosate herbicides these days are blends of several pesticide ingredients in addition to the glyphosate. Be sure you are using a product that is appropriate for veggie gardens and doesn't have long-lasting effects.