The asymptotic stability of the zero solution of autonomous systems of differential equations is considered. For systems satisfying the Barbashin-Krasovskii theorem positive-definite functions are constructed having a negative-definite derivative. The investigation is based on the method of invariant relations. © 2008 Elsevier Ltd. All rights reserved.
Kovalev, A. M. (2008). The construction of Lyapunov functions with sign-definite derivative for systems satisfying the Barbashin-Krasovskii theorem. Journal of Applied Mathematics and Mechanics, 72(2), 164–168. https://doi.org/10.1016/j.jappmathmech.2008.04.008