On the optimal speed problem for the class of linear autonomous infinite-dimensional discrete-time systems with bounded control and degenerate operator

The solution of the minimal-time problem of for the class of linear discrete-time systems with infinite-dimensional state vector and singular operator is considered. The statements of the properties of convex sets are formulated and proven. The necessary and sufficient conditions of optimality is given in the case when origin belongs to boundary of the reachability set. Optimality conditions are given in form of discrete maximum principal. Singular character of maximum principal for the interior point is proven. Algorithm for solving the minimal-time problem for the interior point is developed. It is based on the reduction to the case of the boundary point.