From UCIPM
(http://ipm.ucanr.edu/PMG/PESTNOTES/pn74121.html):
"Perennial pepperweed is less affected by tarping and solarization than annual species due to its large perennial root structure. Research with tarping has been inconsistent. The best control with tarping was obtained using thick, black plastic secured over the infested area for two growing seasons. Mowing and tilling the site before tarping can improve control compared with mowing and tarping alone. It is important to extend the plastic tarp at least 10 feet on all sides of the infested area as creeping roots can spread laterally up to 10 feet. Tent solarization can be used to kill seeds and roots after hand pulling if disposal of pulled plants is not possible."
-Jordan Isken