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

Abstract: Lyapunov functionals are used usually for stability investigation of systems with aftereffect. The general method of Lyapunov functionals construction which was proposed and developed by Kolmanovskii and Shaikhet 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. Keywords: Difference equations, Method of Lyapunov functionals construction, Asymptotic stability. 1. STATEMEN