Approximation of asymptotic stability domain for differential-difference systems with time delay

The asymptotically stability domain for nonlinear systems of differential-difference equations is approximated by the domain of asymptotically stability for difference equation systems. The algorithm for estimating the asymptotically stability domain for a difference system is developed and it is based on the Lyapunov-Krasovskii functional method. The method of asymptotically stability domain mapping in functional space is proposed. An example is given to illustrate the method.