Discretization of Second Lyapunov Method

Abstract

We propose a new criterion of stability in the sense of Lyapunov of the equilibrium point of autonomic differential equations using discrete approach. This approach includes a consideration of a family of hypersurfaces instead of the Lyapunov functions, and conditions on the right-hand part of the differential equation on them instead of conditions on a Lyapunov function along trajectories of the equation.