A method is proposed for finding reachable values of the output vector, taking into account constraints on the input and output signals during the control process for linear discrete systems with variable parameters. The developed algorithm overcomes the computational limitations of traditional approaches when working with high-order models. The method is based on sequential analysis of the output vector components by reducing them to linear programming problems. Its application is demonstrated using the example of the Globus-M2 spherical tokamak plasma model, where the possibility of determining attainable plasma configurations under constraints on the control voltages and currents is shown.