You can also attack perennials with herbicides or organic weed-killing chemicals. In late summer and early fall they begin moving carbohydrates down into their root systems for winter storage. If you spray those plants during that period, they will naturally carry those chemicals deep into their root networks. That is much more effective at killing roots than applying weed killer in the spring.

I've been meaning to do this to Japanese Knotweed at my neighbor's fence, if not elsewhere in the neighborhood.