Collective Pursuit with Integral Constraints on the Controls of Players

Under consideration is a linear differential game of several persons with integral constraints on the controls of the players. Pursuit terminates if a solution to at least one of the equations describing the differential game hits the origin at some instant of time. We establish a necessary and sufficient condition of terminating pursuit from all points of the space in the case of a single pursuer and a sufficient condition in the case of many pursuers.