Algorithms for constructing a system of comparison and estimates of the Lyapunov vector function

The purpose of research-based on the Lyapunov vector function and the comparison principle, algorithms were developed and comparison systems were formed for continuous and discrete linear equations that describe complex dynamic systems. In this work, methods for the decomposition of complex dynamic systems into subsystems with linear connections were presented. With the help of such methods, the process of studying complex systems was simplified. In the course of the research, detailed algorithms for constructing a comparison system for continuous and discrete objects of complex systems were also developed. Then, based on N.N. Krasovsky, an assessment of the Lyapunov vector function was considered and conditions for the stability of complex dynamical systems were formed. The developed algorithms support the calculation of the Lyapunov vector function and the construction of a comparison system for continuous and discrete objects of complex dynamic systems. This is the basis for assessing the stability of the system and the influence of linear relationships on the stability of the system. In addition, on the basis of these algorithms (decentralization of complex systems and the construction of a comparison system), the synthesis of control of complex dynamic systems is implemented. In this work, algorithms have been used to analyze the sustainability of an electric power pool.