On the problem of stability of a motion of essentially nonlinear systems


  • A.A. Martynyuk S.P. Timoshenko Institute of Mechanics of the NAS of Ukraine
  • V.O. Chernienko S.P. Timoshenko Institute of Mechanics of the NAS of Ukraine




estimation of the Lyapunov function, essentially nonlinear system, motion, resistance to large disturbances


This article discusses essentially nonlinear systems. Following the approach of applying the pseudolinear inequalities
developed in a number of works, new estimates for the variation of Lyapunov functions along solutions
of the considered systems of equations are obtained. Based on these estimates, we obtain sufficient conditions
for the equiboundedness of solutions of second-order systems and sufficient conditions for the stability of an
essentially nonlinear system under large initial perturbations. Conditions for the stability of affine systems are
also obtained.


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How to Cite

Martynyuk, A., & Chernienko, V. (2021). On the problem of stability of a motion of essentially nonlinear systems. Reports of the National Academy of Sciences of Ukraine, (2), 3–12. https://doi.org/10.15407/dopovidi2021.02.003