Построение функции Ляпунова при выполнении теоремы Барбашина–Красовского

Abstract

The paper presents a method of building a strong Lyapunov function from a weak one for autonomous systems satisfying the conditions of the Barbashin–Krasovskii theorem. The method is based on results from the invariant set theory. The resulting function is built iteratively as a sum of the initial Lyapunov function with semidefinite derivative and several additional functions, whose derivatives have definite signs at the points, where the derivative of the initial function becomes zero.