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We study the properties of the maximum set for practical weak stability of discrete inclusions. The properties of boundary and interior points and compactness of the set of initial data are proved. The Minkowski function, the inverse Minkowski function, and the support function are obtained for discrete linear inclusions.

The paper suggests an approach to modeling of industrial enterprises providing production according to the set standard with admissible tolerances and requirements. The mathematical model has the form of a discrete control system. We use the properties of generalized inverse matrices to design the control. We present an algorithm of the control of a production process providing release of production. This approach allows to simulate the technological processes (including metallurgical, chemical, energy, etc.) and gives the operating conditions under the constant influence of internal and external destabilizing factors.

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