Journal of Mathematical Sciences

, Volume 190, Issue 4, pp 567–588 | Cite as

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

Article

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.

Keywords

Asymptotic stability auxiliary functions with sign-constant derivatives Lyapunov function theorems of Barbashin–Krasovskii and Matrosov construction of the Lyapunov function on their basis 

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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Institute of Applied Mathematics and MechanicsNASUDonetskUkraine

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