On global asymptotic stability of solutions of a system of ordinary differential equations

Abstract

To investigate global asymptotic stability in general of an equilibrium position of an autonomous system of ordinary differential equations, considered by V.A. Pliss, a function different from the Lyapunov functions is applied. V.A. Pliss proved that for this system it is impossible to construct the Lyapunov function as a sum of a quadratic form and an integral of some nonlinear function defined by the right-hand side of the system.To investigate global asymptotic stability in general of an equilibrium position of an autonomous system of ordinary differential equations, considered by V.A. Pliss, a function different from the Lyapunov functions is applied. V.A. Pliss proved that for this system it is impossible to construct the Lyapunov function as a sum of a quadratic form and an integral of some nonlinear function defined by the right-hand side of the system.