The main objective of this work is to propose a novel paradigm for the design of two layers of control laws for DC-bus microgrids in islanded mode. An intensive attention will be paid to the inner control level for the regulation of DC-DC electronic power converters, where the use of Hybrid Dynamical System theory will be crucial to formulate and exploit switching control signals in view of reducing the dissipated energy and improving system performance. Indeed, this recent theory is well suited for analysis of power electronic converters, since they combine continuous (voltage and currents) and discrete (on-off state of switches) signals avoiding, in this way, the use of averaged models. Likewise, an outer control level for controlling DC-bus microgrids will be developed to provide a distributed strategy that makes the microgrid scalable and robust with respect to blackouts of sources and/or loads, following the principle of t Multi-Agent System theory. In this distributed strategy, they are several crucial and innovative aspects to be regarded such as the different converter architectures, the hybrid and nonlinear nature of these converters. Stability properties are guaranteed by using singular perturbation analysis.