On the Method for Refining A Priori Estimates of the Objective Function in the Speed-in-Action Problem for a Linear Discrete-Time System

A two-dimensional linear discrete-time system with bounded control is considered. The speed-in-action problem for a given system is studied, in particular, the issues of a priori estimation of the minimum number of steps required to transfer the system from the initial state to the origin of coordinates are studied. The method for systems with a diagonalizable matrix is proposed for constructing effective estimates of the optimal value of the objective function in the speed-in-action problem as a function of the initial state. Sufficient conditions are formulated under which these estimates cannot be improved. Numerical calculations are presented.