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In this paper, we give a detailed analytical study of a two-cell dc-dc buck converter. We analyse the dynamics of the system by using a discrete time modelling approach and considering a digital controller. This controller includes a dynamic compensator in the form of a digital integrator for the output variable regulation. The discrete time model for the whole system is used to predict the instability of the system when some design parameters are varied. To facilitate the design, an approximated closed form discrete time model is derived in the form of a recurrence equation which accurately describes the dynamical behavior of the system. The Jury test is applied to the characteristic polynomial in order to obtain stability boundaries in the design parameter space. Some design rules to obtain optimal transient behavior are also given. Numerical simulations and experimental measurements confirm the theoretical predictions.