Некоторые актуальные направления научных исследований в области теории устойчивости динамических систем

Translated title of the contribution: SOME ACTUAL DIRECTIONS OF SCIENTIFIC RESEARCH IN THE FIELD OF THE STABILITY THEORY OF DYNAMICAL SYSTEMS

Research output: Contribution to journalArticlepeer-review

Abstract

The paper deals with stability of solutions of nonlinear dynamical systems with complex changing structure of connections. The main results of stability analysis by means of nonlinear approximation are presented. Important aspects of applying the theory of differential inequalities and the method of comparison to stability analysis are described. The question of construction of auxiliary comparison systems for the considered dynamical systems is studied. Stability criteria for those comparison systems are formulated. Methods of decomposition and aggregation of complex systems are considered. The switches influence on stability is estimated. Some directions of classical results development, relevant in recent years, are shown. In particular, these results are applied to the problem of absolute stability, the modeling of population interactions in biological communities, and the stability analysis of the equilibrium positions of mechanical systems.
Translated title of the contributionSOME ACTUAL DIRECTIONS OF SCIENTIFIC RESEARCH IN THE FIELD OF THE STABILITY THEORY OF DYNAMICAL SYSTEMS
Original languageRussian
Pages (from-to)17-29
JournalПроцессы управления и устойчивость
Volume6
Issue number1
StatePublished - 2019

Keywords

  • STABILITY OF MOVEMENT
  • NONLINEAR SYSTEMS
  • COMPLEX AND HYBRID SYSTEMS
  • Lyapunov methods
  • NONLINEAR APPROXIMATION STABILITY

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