Best time to kill many perennial weeds and invasive plants with weed killer? Late Summer and Autumn!
Post contains content updated on August 20, 2018:
I remind people every year that late summer and fall are great times to apply herbicides to kill perennial invasive plants. I have discussed the timing of herbicide applications in several previous posts. So, get out and enjoy that cooler weather (it will come) and, for those of us farther north, beautiful fall colors!
In terms of priority, I would put perennial weeds into three groups for purposes of application timing: First are the perennials that need to be treated before a frost. Plants such as bindweed, crown vetch, and Japanese knotweed, die back after a frost. Therefore they need to be treated in late summer or early fall before a killing frost.

Aquatic foam herbicide applied to invasive knotweed in September

Foam weed killer applied in September to invasive crown vetch. Note that the crown vetch has been bunched into a pile to improve targeting.
Second are the plants such as perennial thistles. Canada thistle is a prime target. Canada thistle can be treated a little later in the fall because it is more frost tolerant. In fact, this frost tolerance can be used to your advantage. If nearby desirable plants have died back or lost their leaves, you can apply herbicide to the thistle with less potential for damage to the desirable plants. Just make sure you apply the herbicide to foliage that is still green.

Foam weed killer applied to Canada thistle in late October after a frost.
Third are the woody perennial weeds. These can be treated with cut stem or frill treatments from the fall into late winter (just do it before warm temperatures start pushing plant sugars up to the branches for leaf out). The application should be into the vascular system of the tree or shrub, e.g., cut stump, frill, or injection. The Directions for the Green Shoots Foam Herbicide System show how to do these applications.
You can also do foliar applications to woody perennials in the late summer and fall. Timing can be a little tricky: if you have had a drought, the leaves of the weed tree may be sparser and may not absorb the herbicide as well.