This paper presents the modeling and control of a multilevel DC/DC bidirectional converter suitable for medium voltage and medium power applications, with a special interest in renewable applications. The multilevel converter is based on Dual Active Bridge (DAB) and its average dynamic model. Two different control strategies are addressed in this paper in order to achieve the overall control of the DC/DC converter: a bilinear systems' control based on quadratic feedback control, and a nonlinear control based in Lyapunov theory. System's controllability and stability are studied, in particular by the analysis of zero dynamics. The performance of both controllers are illustrated by computer simulations, and the concluding remarks analyze theirs characteristics and draw some comparisons.