Inverter-based resources (IBRs) introduce fast dynamics and high non-linearities to microgrids, degrading their stability and complicating the design of effective controllers. To address the arising vulnerability and non-linearities, this paper presents a systematic controller design approach that ensures large-signal stability and domain of attraction (DOA) for islanded microgrids. First, the nonlinear electromagnetic transient model of inverter-based microgrids is developed in the rotating dq reference frame, which is then transformed to a homogeneous-like system with nonlinear terms acting as superimposed parameter uncertainties. Next, the stability conditions, including certified stability, certified DOA, and their combination, are derived to rigorously guarantee a designated range to be a subset of DOA. The designated region is customized and flexible enough to cover microgrids’ normal or emergency operational ranges, such as low- and high-voltage ride-through (L/HVRT) conditions. Then, a systematic method for identifying the candidate control parameter set is developed by integrating the analytical stability conditions. This approach is further exemplified in the droop controller design to improve microgrid stability and resilience. Finally, the proposed systematic controller design is verified through numerical simulation and power hardware-in-the-loop experiments to ensure large-signal stability and DOA of microgrids in emergency L/HVRT conditions.