The increasing adoption of power electronic devices may lead to large disturbance and destabilization of future power systems. However, stability criteria are still an unsolved puzzle, since traditional small-signal stability analysis is not applicable to power electronics-enabled power systems when a large disturbance occurs, such as a fault, a pulse power load, or load switching. To address this issue, this paper presents for the first time the rigorous derivation of the sufficient criteria for large-signal stability in DC microgrids with distributed-controlled DC-DC power converters. A novel type of closed-loop converter controllers is designed and considered. Moreover, this paper is the first to prove that the well-known and frequently cited Brayton-Moser mixed potential theory (published in 1964) is incomplete. Case studies are carried out to illustrate the defects of Brayton-Moser mixed potential theory and verify the effectiveness of the proposed novel stability criteria.