Development of the Theoretical Approach Based on Matrix Theory for Analyzing the State of Information Security Systems

The widespread introduction of information technologies into all spheres of society, the creation of a significant amount of confidential and critical data in digital form leads to an increase in the priority of information security tasks everywhere, including in the energy sector, which relates to the critical infrastructure of any state. The purpose of the work is to develop the mentioned ap-proach to ensure the possibility of increasing the efficiency of information security methods based on it. The goal was achieved through a detailed study of disturbances in the values of formal parameters that uniquely determine the matrix that is assigned to the information security system under conditions of active attacks (disturbances) on the system. Singular numbers and singular vectors of the matrix are considered as such parameters. The most important result of the work is the substantiation of the existence and establishment of interconnected regions of stabilization of disturbances of singular numbers and singular vectors of the system matrix, while the region of stabilization of singular numbers corresponds to the region of monotonous decrease in their disturbances with increasing numbers, while the stabilization of singular vectors corresponds to the region in which their disturbances are comparable with 90 degrees. It is shown that the stabilization process is determined by the mathematical properties of the parame-ters under consideration. The significance of the obtained result lies in the possibility of using it to improve various information security systems that are built or studied using a general ap-proach to analyzing their state, both theoretically and practically. The work provides examples of such use.