The grass in your photos appears to be Bermudagrass or Zoysia grass which are both warm season grasses. Both prefer sun and are drought tolerant. Both can spread fairly aggressively due to their ability to grow via above ground stems (stolon) and below ground stems (rhizomes).

Bermudagrass leaves are generally smooth and pointed with a conspicuous ring of white hairs where their blades meet the sheath and have a sheath at each node and can produce flowering stems or seed heads. It is not easy to control but can be managed nonchemically with regular removal from a pre-established lawn and by withholding water during the summer to dry out the stolons and rhizomes. It can also be managed chemically through the use of grass selective or nonselective herbicides. 

Zoysia has a similar appearance with hairs that are instead standing upright on the leaf blade. It will be stiff to the touch and can withstand foot traffic and mowing better than bermudagrass. It will have a vibrant green (almost lime green) color, but goes dormant (browns and has a dead appearance) in the fall/winter. 

Below are links to additional information about these types of grasses and methods of control:

https://www.canr.msu.edu/news/zoysiagrass_a_warm_season_grass_in_a_cool_season_world

https://www.turffiles.ncsu.edu/grasses/zoysiagrass/

https://hgic.clemson.edu/factsheet/zoysiagrass/

https://turf.purdue.edu/common-bermudagrass/

https://ipm.ucanr.edu/pmg/pestnotes/pn7453.html

https://www.pubs.ext.vt.edu/content/dam/pubs_ext_vt_edu/spes/SPES-350/SPES-350.pdf