In this paper we investigate the nonlinear dynamics of a bidirectional boost converter by employing a nonlinear analysis method based on the Monodromy matrix. This approach can be used to study the influence of system parameters for the stability of power electronics systems. Specifically, it is applied to address and control the fast-scale instability phenomena of power converters for different input and loading conditions. This can be achieved as all the necessary information, such as system input, load, converter parameters and coefficients of the control loop are utilized in the derivation of the Monodromy and Saltation matrices. Moreover, the adopted approach is design-oriented which operates in a more straightforward way compared to other nonlinear analysis methods. Based on the derived matrices, a supervising controller is designed to control the nonlinear behavior of the system, which improves the system performance significantly. Simulation results show the effectiveness of this method.