This paper presents a nonlinear analysis method to investigate the influence of parameter variation on the stability of interleaved boost converters. The Saltation and the Monodromy matrices are employed to fully unfold and understand the inherent nonlinear dynamics of interleaved boost converters. Moreover, using the knowledge gained from this analysis it is possible to design controllers that guarantee a satisfactory performance of the converter avoiding fast and slow scale bifurcations. This methodology has been previously employed on single-stage DC-DC converters by the authors but now it will be expanded in multilevel interleaved boost converters. In the proposed approach, the interaction effect of switching operation can be analyzed. Meanwhile, all the comprehensive information of converter parameters and control loop are introduced in the derivation of the Monodromy matrix, which can be used for further stability analysis. Numerical and analytical results validate our work.