The robustness of control is a requirement to maintain a fluid layer at conductive equilibrium heated to a highly supercritical condition. Robustness determines how much uncertainties, or design parameter mismatches, can be tolerated. Both linear stability analysis and three-dimensional fully nonlinear simulations are used for the study of the linear quadratic Gaussian (LQG) controller. The parameter mismatches from the nominal conditions are introduced into the plant model, while the LQG compensator assumes nominal conditions. The mismatches arise from boundary properties, actuator lag, sensor level uncertainty, and wall thickness, as well as from the major parameters such as Prandtl number, Rayleigh number, wave number, and truncation number in the reduced-order model. The results suggest that the LQG compensator action can preserve closed-loop stability at over ten times the critical Rayleigh number, provided that the mismatches in the sensor level and wall thickness are small. Mismatches in the Prandtl number and wall material properties have little impact. Mismatches in Rayleigh number and wave number are relatively benign compared with the sensor and thickness parameters. Techniques for measuring the plant output temperature at multiple levels with sufficient accuracy may be an implementation challenge.