UDC 517.93
TECHNOLOGICAL APPROACH TO THE RESEARCH OF DYNAMIC SYSTEMS STABILITY: SYSTEM ANALYSIS OF DYNAMIC PROCESSES STABILITY
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.
In the system analysis of dynamic models an essential role is played by the questions connected with the analysis of dynamic systems balance provision stability, and in their mathematical models – stability of equations systems solutions. Technical "stability" is a capability of system to return to an equilibrium condition after third-party indignation or management. The direct method of Lyapunov remains the major one for the research of dynamic systems stability. However, heuristic creation of Lyapunov function isn't connected directly with structural properties of the researched system and therefore there are no exhaustive general methods of its creation on the set system model yet. It is the most serious lack of Lyapunov methodology. In the work this shortcoming is overcome: two fundamental problems of the system analysis of dynamic systems are considered: creation of Lyapunov type functions according to a system model and assessment on this basis of stability area (asymptotic stability) of a dynamic system.
The work aim is to offer technological, algorithmically implementable method of creation of functions of Lyapunov type for the analysis of real dynamic systems stability on their models. Properties of the offered approach are considered. The method is approved on the systems described by Lyenar, Van der Paul, La-Sall's equations and showed the outstanding performance.
Key words: system analysis, dynamic processes, stability, Lyapunov type functions, Lyenar, Van der Paul, La-Sall's system.