An analysis is presented on the feasibility issue in command governor (CG) control with deterministic set-membership state estimators for determining the state uncertainty set (SUS), viz. the set of all states which are compatible with measurements and a priori knowledge on the system. It is shown that the recipe of modifying standard receding horizon CG schemes based on the full knowledge of the state is effective provided that the latter is exactly computed at any time. On the contrary, when simple-shaped outer approximations of SUS are exploited for reducing the numerical complexity of the algorithm, loss of solvability or stability may result.