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UDC 517.93

CONSTRUCTIVE APPROACH TO THE RESEARCH OF DYNAMIC SYSTEMS STABILITY: APPLIED PROBLEMS

V. V. Mironov, PhD (physical and mathematical sciences), Professor at the Department of higher mathematics, RSREU; This email address is being protected from spambots. You need JavaScript enabled to view it.
Yu. S. Mitrokhin, PhD (physical and mathematical sciences), Associate Professor at the Department of higher mathematics, RSREU; This email address is being protected from spambots. You need JavaScript enabled to view it.

The questions related to the behavior of equilibrium points of dynamical systems analysis, and in their mathematical models – systems of equations solutions stability were systematically considered in the work. "Stability" is understood as the ability of a system to return to equilibrium after third-party disturbance. The construction of the Lyapunov function is not associated with the structural properties of the system, there is still no comprehensive general methods of its construction for a given model of the system. This drawback was overcome in the first part of the paper, and there were solved two fundamental problems of the system analysis of dynamic systems. They are 1) building a Lyapunov type function by system model, and 2) evaluating the region of stability (asymptotic stability) of the dynamic system.

The aim of the second part of work: to approve the technological method offered in the first part of work for the analysis of real dynamic systems stability on Lyenar, Van der Paul, La-Sall models and their modifications and to show efficiency of the method.

Keywords: system analysis, dynamic processes, stability, Lyapunov type functions, Lyenar system, Van der Paul system, La-Sall system.

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