On 0-controllability and pursuit problems for linear discrete systems under total constraints on controls - Kuchkarov, Atamurat; Ibragimov, Gafurjan; Sotvoldiev, Akmal (Springer Singapore, 2013)
We consider linear discrete control and pursuit game problems. Control vectors are subjected to total constraints, which are discrete analogues of the integral constraint. By definition, (i) the control system is 0-controllable on the whole if there is a control such that the state of the system z(t) = 0 at some step t, (ii) pursuit can be completed if there exists a strategy of the pursuer such that for any strategy of the evader the state of the system y(t) = 0. We obtained sufficient condition for equivalence of 0-controllability and completion of the game from any initial position of the space.