Stability under Persistent Disturbances of Impulsive Differential-Difference Equations of Neutral Type

Effective sufficient conditions for stability under persistent disturbances of the zero solution of impulsive systems of differential-difference equations of neutral type are found. The main results are stated in a theorem. In its proof an analogue of Gronwall-Bellman′s inequality for piecewise continuous functions is used. As a corollary the existence of a global solution of a system with quadratic nonlinearities is proved for sufficiently small initial data.