Herbicide in Food Manufacturing Plant
There should be no issue doing this , and to ensure the area doesn't return to this state, have a 2 foot wide section cleared of grass etc, landscape fabric put down and then stone. The you'll only have the occasional weed to pull
Make sure that the chemical is stored in an area that it is not going to become a hazard to your process.
I always try and have our pest control companies do herbicide treatments. It means I don't have to have training docs for maintenance personnel to apply it, I don't have to deal with storing it and have any debate as to whether it's secure enough to prevent disgruntled employees from getting it, and I don't have to deal with maintenance guys who decide "I found a better weed killer at the store, so I brought a few different bottles" and end up with chemicals that aren't on my approved register. Way easier to say "this plant does not store or apply pesticides/herbicides" in my GFSI audits.
That said, you absolutely can keep herbicides. They'll ideally be kept with maintenance, in a completely separate locked storage cabinet that does not comingle any food grade lubricants or chemicals, and you'll train all employees who handle chemicals that herbicides are never to be used by unauthorized persons and never inside the plant itself.
You stated using them "within the perimeter of a food manufacturing plant". Are you saying inside the actual building?