A new way to approach robust Dynamic Inversion controller synthesis is addressed in this paper. A Linear Quadratic Gaussian outer-loop controller improves the robustness of a Dynamic Inversion inner-loop controller in the presence of uncertainties. Desired dynamics are given by the dynamic compensator, which shapes the loop. The selected dynamics are based on both performance and stability robustness requirements. These requirements are straightforwardly formulated as frequency-dependent singular value bounds during synthesis of the controller. Performance and robustness of the designed controller is tested using a worst case time domain quadratic index, which is a simple but effective way to measure robustness due to parameter variation. Using this approach, a lateral-directional controller for the X-38 vehicle is designed and its robustness to parameter variations and disturbances is analyzed. The controller analysis is extended to the nonlinear system where both control input displacements and rates are bounded. Overall, this combination of controller synthesis and robustness criteria compares well with the usynthesis technique. It also is readily accessible to the practicing engineer, in terms of understanding and use.