My solution for an area of about 5x10 feet full of this stuff was to rent an industrial strength brush whacker/cutter and cut all this stuff down to ground level. Then I brought in 1/2 cubic yard of topsoil spread it out over the area and seeded that.
I let the grass grow for about 2 months and could see it was grass and also full of the root suckers.
Then i started mowing. The suckers kept coming back for a period of time, but was mowed down with the grass. Now the area is all grass, and looks nice.