Dual active bridge is often considered in many dc/dc converter applications where high efficiency, input/output voltage ratio, and power level are required. Recently, a predictive control technique, named moving discretized control set model predictive control has been introduced, in order to achieve faster dynamics and stable operation throughout the power and terminal voltage ranges, considering global control parameters. However, even if this technique provides flexible multi-objective control, its large signal stability remains in questions. In this article, the proposed control design is described in detail, and its large signal stability is analyzed, considering the case of a dual active bridge converter operating in single-phase shift. The obtained results show insights into factors that stabilize or destabilize the converter operation. The proposed control and stability analysis is validated through both simulation and experimental testing.