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Direct method of impulsive systems after Liapunov and its application within the research of critical state of equilibrium

Work number - M 7 AWARDED

Slynko Vitaly Ivanovych “

introduced by S. P. Timoshenko institute of mechanics NAS of Ukraine for annual award of the president of Ukraine for young scientists.


The aim of work is the research of stability in nonlinear impulsive systems in particular the critical cases for such systems. The scientific innovations of the research are: the new synthesis for theorems of Liapunov`s direct method for pseudo-linear systems differential equations and sufficient conditions of stability in critical states of equilibrium impulsive systems, the determination of sufficient conditions of trivial form of stability nonlinear systems with impulsive action, that are monotonous as regard to some cone, and in particular comparison systems, including abstract differential equations. The sufficient conditions of stability in linear equations with impulsive action and delay are determined as well. The new methods are proposed to research the impulsive model systems of Takagi-Sugeno. The sufficient conditions of robust stability of the linear periodic impulsive systems are obtained. The sufficient conditions stability of critical state of equilibrium are ascertained in one case that is analogical to case that has been had G. V. Kamenkov. The results are applied for research of stability the states of equilibrium in some mechanical systems with impulsive action. The practical use of results is within the possibility of application in researches of mathematical models of complex systems.

Author`s researches are published in such international academic periodicals with nonzero impact-factor as: Mathematical Notes, Sbornik: Mathematics, Siberian Mathematical Journal, Ukrainian Mathematical Journal, Nonlinear Oscillations, Differential Equations,  Automation and Remote Control, ‘Int. J. of Innovative Computing, Information and Control”, Journal of Computer and Systems Sciences International, Applied Mechanics, Siberian Journal of Applied and Industrial Mathematics.

Total amount of citations (SCOPUS)—76. The author`s h-indexis 6. The introduced results for awards competition works are published in 21 scientific researches in specialized academic periodicals. There are 18 scientific researches published in international academic periodicals that