Functional stability of production processes as control problem of discrete systems with change of state vector dimension

The paper proposes an approach to mathematical modeling of technological processes of industrial enterprises for the organization of production in accordance with established standards with compliance with acceptable tolerances and requirements. For the first time, the authors consider the property of functional stability of production processes in two aspects: as a property of the system to maintain its functional state under conditions of change and as a property of the system to restore its functional state after the effects of external and internal factors (functional stability and functional resilience). We presents the mathematical model of production processes in the form of linear discrete control systems under the following condition: the state vector changes dimension. This condition shows that the parameters characterizing the state of the system can change at different stages of production processes due to technological features. This causes the state vector dimension to change. The authors give definition of functional stability of the process, prove theorems on conditions of functional stability and give solution of control design problem using generalized inverse matrices properties.