On the Modified Third Method in the Pursuit Problem for Differential-Difference Equations of Neutral Type

In this paper, we study linear differential games described by a system of linear differential-difference equations of neutral type under geometric constraints on the controls of the players. Modified third method in the pursuit problem and modified method of directional pursuit are established for differential-difference equations of neutral type. We obtain new sufficient conditions on parameters of the process guaranteeing finishing the game in a definite finite time.