Aerospace and shipboard power systems, as well as merging terrestrial microgrids, typically include a large ercentage of regulated power-electronic loads. It is well nown that such systems are prone to so-called negative- mpedance instabilities that may lead to deleterious scillations and/or the complete collapse of bus voltage. umerous small-displacement criteria have been developed o ensure dynamic stability for small load perturbations, and echniques for estimating the regions of asymptotic stability bout specic equilibrium points have previously been established. However, these criteria and analysis techniques o not guarantee system stability following large nd/or rapid changes in net load power. More recent research as focused on establishing criteria that ensure arge-displacement stability for arbitrary time varying loads rovided that the net load power is bounded. These yapunov-based techniques and recent advancements in eachability analysis described in this thesis are applied to xample dc and ac microgrids to not only introduce a large- isplacement stability margin, but to demonstrate that the elected systems can be designed to be large-displacement table with practicable constraints and parameters.