This paper presents a methodology based on two interrelated rapid prototyping processes in order to find the best correspondence between theoretical, simulated, and experimental results of a power converter controlled by a digital PWM. The method supplements rapid control prototyping (RCP) with effective math tools to quickly select and validate models of a controlled system. We show stability analysis of the classical and two modified buck converter models controlled by zero average dynamics (ZAD) and fixed-point induction control (FPIC). The methodology consists of obtaining the mathematical representation of power converters with the controllers and the Lyapunov Exponents (LEs). Besides, the theoretical results are compared with the simulated and experimental results by means of one- and two-parameter bifurcation diagrams. The responses of the three models are compared by changing the parameter K_s of the ZAD and the parameter N of the FPIC. The results show that the stability zones, periodic orbits, periodic bands, and chaos are obtained for the three models, finding more similarities between theoretical, simulated, and experimental tests with the third model of the buck converter with ZAD and FPIC as it considers more parameters related to the losses in different elements of the system. Additionally, the intervals of the chaos are obtained by using the LEs and validated by numerical and experimental tests