The dual active bridge (DAB) converter has been widely used in the distributed power systems and the energy storage devices. However, the inherent nonlinearity of the DAB converter can cause serious stability problem. In this paper, the dynamics of a digital controlled DAB converter with output voltage closed loop control is studied. Firstly, to accurately study the nonlinear dynamics and stability in a DAB converter, a full discrete-time model for the DAB converter is established. The model considers the ESR of the output capacitor and also considers the digital control delay and sample-and-hold process. Using this model, the stability of the DAB converter versus the parameter of the proportional controller is analyzed and the stability boundary is accurately predicted. Further, this paper also points out that the ESR of the output capacitor can bring a great effect to the stability of the system. Finally, simulation and experimental results verify the theoretical analysis.