Numerical method for solving the time-optimization problem for linear non-stationary discrete-time systems of general form

In the paper, we construct a software-implemented numerical procedure for solving the time-optimization problem for linear discrete-time systems with arbitrary variable matrices of the system and convex sets of geometric constraints on control. We also prove the convergence of the sequence of control processes produced by the algorithm to a solution to the problem. The efficiency is demonstrated on a number of examples.