Method of Radial Drift for Qualitative Study of the Properties of the Nonlinear Dynamic Systems. II. Study of Asymptotic System Stability

The method of monotonic radial drift proposed in the first part of this paper was used to study the conditions for asymptotic stability (in large) of the equilibrium states of dynamic nonautonomous nonlinear systems of an arbitrary order. It enabled the author to obtain new conditions for asymptotic stability of these states which allow one to carry out studies mostly on the basis of direct information about the right-hand side of the system. The method enables one to study systems to which neither the first nor second Lyapunov method is applicable.