, Volume 190, Issue 4, pp 567-588
Date: 27 Mar 2013

On the construction of the Lyapunov function with sign-definite derivative with the help of auxiliary functions with sign-constant derivatives

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Abstract

The short survey of studies of the asymptotic stability with the help of auxiliary functions (positive definite and nonnegative) whose derivatives are nonpositive by virtue of the equations of perturbed motion and the construction of positive definite Lyapunov functions with negative definite derivatives on the basis of these auxiliary functions is given. The example of the construction of the Lyapunov function with the use of an auxiliary nonnegative function with nonpositive derivative is presented.

Presented by A. M. Samoilenko
Translated from Russian by V. V. Kukhtin
Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 9, No. 4, pp. 515–545, October–November, 2012.