On the problem of operation speed for the class of linear infinite-dimensional discrete-time systems with bounded control

Consideration was given to the problem of operation speed for the class of linear autonomous systems with infinite-dimensional state vector. The statements about the properties of the Minkowsky sum for the convex sets were formulated and proved. For the boundary points of the $0$-controllability set, the necessary and sufficient conditions for solvability of the problem of operation speed were established. The optimality conditions were set down for the boundary points in terms of the discreet principle of maximum. Nonuniqueness of the optimal control and degenerate nature of the principle of maximum were proved for the internal points. An algorithm to solve the problem of operation speed for the internal points was developed by reducing it to the allowed case of the boundary points. Examples were given.