Abstract
We present methods for proving new sufficient stability and asymptotic stability tests for the zero solution of a time-varying differential equation using nonmonotone sign-indefinite Lyapunov functions. As an example of application of our statements, we establish new stability tests for a gradient system in which the equilibrium is not isolated and the function defining the right-hand side does not have a minimum at the equilibrium point. A stability test for a Hamiltonian system is indicated for the case of a nonstrict minimum of potential energy at the equilibrium point.
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Translated by V. Potapchouck
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Knyazhishche, L.B. Solution Stability Conditions for Differential Equations with Nonmonotone Lyapunov Functions. Diff Equat 57, 165–172 (2021). https://doi.org/10.1134/S0012266121020051
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DOI: https://doi.org/10.1134/S0012266121020051