Dual　active　bridge　(DAB)　converters　have　been　widely　used　in　distributed　power　systems　and　energy　storage　equipment.　However,　the　inherent　nonlinearity　of　the　DAB　converters　can　cause　stability　problem,　such　as　output　voltage　oscillation.　In　this　paper,　the　dynamic　behavior　and　stability　of　a　digitally　controlled　DAB　converter　with　a　closed-loop　controller　are　studied.　First,　to　accurately　study　the　nonlinear　dynamics　and　stability　in　a　DAB　converter,　a　bilinear　discrete-time　model　considering　the　output　capacitor　equivalent　series　resistance　(ESR)　and　the　digital　control　delay　in　circuit　is　established.　Based　on　the　model,　the　nonlinear　dynamic　characteristic　and　stability　of　the　DAB　converter　versus　the　control　parameter　are　studied.　Furthermore,　extensive　analyses　are　performed　to　study　the　effect　of　the　transformer　leakage　inductance　and　the　output　capacitor　ESR　on　the　stability　boundaries　of　the　control　parameter.　The　accuracy　of　the　model　and　the　theoretical　analyses　are　validated　by　simulation　and　experimental　results.　The　proposed　model　of　the　digitally　controlled　DAB　converter　can　accurately　predict　the　stability　boundaries,　which　can　be　effectively　applied　to　the　design　of　the　system　parameters　and　guarantee　stable　operation　of　the　converter.