Abstract
Modern ideas about socio-economic systems as systems of high complexity determine the search for management models that can develop adaptive properties to ensure their flexible maneuverability in an environment filled with fluctuations of different categories and uncertainty of the behavior of its subjects. Adaptation, according to the laws of evolution, is carried out within a certain limit, where actions are considered as a threshold response to changes. In the article, the limit is con sidered as a developing concept, starting from the philosophical interpretation, mathematical representation and purpose in management. Methods for determining the limit as a numerical sequence, represented as an information granule, using methods of mathematical statistics and fuzzy set theory are generalized. The causality of the transition from a feedback control model formed by significant deviations to a robust control model with predicted variants of the system maneuvering trajectory in the environment is revealed. A methodological approach to the definition of a robust limit as a numerical sequence (set), its structure, with the definition of a qualitative assessment of subsets in the contours of which a socio-economic system should exist and successfully develop with the use of a robust control mechanism, is presented.