Global Asymptotic Stability with Respect to Part of the Variables for Solutions of Systems of Ordinary Differential Equations

Abstract

We propose a new approach to studying the global asymptotic stability of an equilibrium position of a system of ordinary differential equations with respect to part of the variables. New functions, different from Lyapunov ones, are used to study state trajectories of systems of ordinary differential equations and prove the global stability theorem. An application of the theorem to proving the global stability for some systems of ordinary differential equations studied by Krasovskii and Pliss is considered.