Chemical control through soil fumigation and antibiotics (streptomycin, ampicillin, tetracycline and penicillin) has shown little suppression of Ralstonia solanacearum. On the otherhand altering soil pH depending on the time of year has been found effective. For potatoes, lowering the pH to 4-5 in the summer and raising it to 6 in autumn may help to eradicate the pathogen. In addition, crop rotation with resistant crops may also be useful!
Reference
USDA/APHIS/PPQ 2003. Pest Data Sheet. Ralstonia solanacearum race 3 biovar 2. February 12, 2003. USDA/APHIS/PPQ, Center for Plant Health Science and Technology, Plant Epidemiology and Risk Analysis Laboratory, Raleigh, NC.
I'm not a Ralstonia specialist, but from what I heard or read from collegues dealing with this pest, I assume it is almost impossible to eradicate it from soil into which it was introduced. There is evidence that some rotation plants will help, although several of these plants seem to harbour the pathogen asymptomatically. One of the difficulties with these bacteria is that they change phases, and can enter a VBNC (Viable But Non Cultivable) state. Then, it's hard to recover them from soil, although it doesn't mean they're absent, and they can revert back to their normal cultivable state under appropriate 'stress'.
I thus assume that eradication is too ambitious a goal, and that one should rather target population management in soils that have been infested.