Circulation Control (CC) is an effective technique to increase lift and improve aerodynamic efficiency of Unmanned Aerial Vehicles (UAVs). This paper introduces a novel, robust nonlinear controller for the longitudinal flight dynamics of a CC-based fixed-wing Unmanned Aerial Vehicle (UC²AV) that operates in cascaded fashion and takes into account changing mass. The controller consists of a dynamic inversion inner-loop and a μ-synthesis outer-loop controller. CC introduces changes of the aerodynamic coefficients that are difficult to determine using strict mathematical formulas. This creates a specific type of model uncertainty in the UC²AV model, which is tackled by the use of μ-analysis. Simulation results demonstrate the efficacy of the proposed control scheme and the ability of the U C² AV to adapt to challenging CC-on-demand scenarios. The technique can be generalized and applied on CC-based and conventional UAVs, seeking to address uncertainty challenges regarding the aircraft's aerodynamic coefficients.