Unfalsified control is a direct data-driven, plant-model-free controller design method, which recursively falsifies controllers that fail to meet the required performance specification, making them ineligible to actually control the plant. In this paper it is shown that sufficient conditions for stability can be derived for unfalsified control with an ellipsoidal unfalsified set, ellipsoidal unfalsified control (EUC), under the mild assumption that there exists at least some region in the original candidate controller pool, which contains controllers that meet the performance specifications. One of these conditions is a finite number of controller switches, which is guaranteed by imposing a maximum volume ratio between two consecutive ellipsoidal unfalsified sets