Investigation of gobal stability of the equilibrium position of a system of differential autonomous equations with the help of admissible functions

Abstract

To study the global stability of the zero solution, which is a single rest point for a nonlinear system of autonomous differential equations, admissible functions are used. These functions are analogous to Lyapunov functions, but do not coincide with them. Admissible functions can also be used for study the global stability of the zero solution of such systems with respect to part of the variables. An example of the application of such functions to the study of the global stability of the equilibrium state for a second-order nonlinear system is presented. © 2019 Author(s).