need non-invasive plant for front slope.

I have a East facing slope where no lawn mowers can be used. I like to have that area coverd with non-invasive plant or grass which bossom all the 3 seasons. Its about 40'x10' area. Currently its full of plants that I never know of their names. Some of them I trim with the edge trimmer. Since the top portion of the slope has about another 60'x10' lawn grass (so no non-invasive plant), I like to have very good verity or quality of plant grown in the slope. Plant/grass should be tolerant to drought and disease.
TIA
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Calyptocarpus vialis (horseherb) Phylla nodiflora (frogfriut) Phylla incisa (frogfruit)
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