We consider a linear pursuit game of one pursuer and one evader whose motions are described by different-type linear discrete systems. Position of the evader satisfies phase constraints:y∈G, whereGis a subset ofRn. We considered two cases: (1) controls of the players satisfy geometric constraints, and (2) controls of the players satisfy total constraints. Terminal setMis a subset ofRnand it is assumed to have a nonempty interior. Game is said to be completed ifyk-x(k)∈Mat some stepk; thus, the evader has not the right to leave setG. To construct the control of the pursuer, at each stepi, we use the value of the control parameter of the evader at the stepi. We obtain sufficient conditions of completion of pursuit from certain initial positions of the players in finite time interval and construct a control for the pursuer in explicit form.
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