The expert on this issue, for the last several centuries, has been the Catholic Church. They have very strict definitions of demonic possession. They insist on eliminating all other possibilities before concluding demonic possession as a cause. Since the advent of modern psychology, the Church has become even stricter in it's definition, making sure that the case can't be explained by psychological or brain-structural causes.
And yes, there are some confirmed cases.
For more info, please read my hub on healing demonic possession and mental illness, though I don't focus on proving cases; I focus on helping people with what works.