Problems of Linear Discrete Games of Pursuit

In this paper, we consider two problems of linear discrete games of pursuit. In each of them, the terms of the sequence defining the pursuer's control are bounded by some positive number. In the first problem, the terms of the sequence defining the quarry's control are bounded by some positive number and, in the second problem, the sum of the $p$th powers of the terms of this sequence is bounded by a given number. For each problem, we obtain a necessary and sufficient condition for the termination of pursuit from all points in space.