We have some recent research results from Mississippi State University which compare Kudzu control products. The recent noxious weed status in Missouri has created a number of questions. As with all difficult, perennial weeds, the key to controlling Kudzu is persistence. Herbicides need to be applied later in the year, when the plant tends to be sending more "energy" (sugars) downward to the root system. However, applications need to be made while the plant is actively growing- if you spray too late in the year, the plant's metabolism is slow. Single herbicide applications are unlikely to completely control Kudzu, repeated applications over a number of years will be required.
PowerPoint show from Mississippi State University (BEWARE, This is a large file with photos!)
Clemson Kudzu Control Guidesheet