Application of the general method of Lyapunov functionals construction for difference Volterra equations

Abstract

Lyapunov functionals are used usually for stability investigation of systems with aftereffect [1–3]. The general method of Lyapunov functionals construction which was proposed and developed in [4–19] is used here for stochastic second type Volterra difference equations. It is shown that using this method, there is a possibility to construct for a given equation, a sequence of extending stability regions.