Permaculture seems to have quite a lackadazical attitude toward invasive plants. For example, to get rid of blackberries, Bill Mollison suggested throw in apples, then wait twenty years until the apples grow into trees. Then you run in cows or pigs. Even then it takes a while. Not a right-now solution.
Mostly permaculturists suggest "rethinking" the problem. Anyhow, here are some suggestions from Permies.com.
http://www.permies.com/t/7165/...
In my yard (I am in kudzu country) I am fighting kudzu's cousin--wisteria. I think the best suggestion is to cut the invasive off at ground level and cover with cardboard. Aesthetically, you can cover that with mulch. You could make a path along the boader to your bed. Line with cardboard, and cover with the mulch of your choice. This would probably have to be renewed periodically, but it should eventually work to keep the quack grass away. Also, think animals: ducks, goats to graze where you think the source of the quack grass might be. they can be managed with a moveable pen, so they don't get into the parts of the garden you dont want damaged by them.
