A new robust hierarchical plasma magnetic control system with time-varying parameters and cascade circuits for the Globus-M2 tokamak (Ioffe Institute) has been synthesized by means of the linear matrix inequalities (LMI) method. Each control cascade has a separate objective: placing poles of the closed-loop system in the D-region to guarantee robust performance, restriction of the H∞-norm of the transfer function between external disturbances and the plant outputs of the closed-loop system, tracking PF-currents, CS-current, plasma current, plasma position, gaps between the plasma separatrix and the first wall. Control cascades were synthesized for an array of plant linear models corresponding to reconstructed plasma equilibria at different time points of the tokamak discharges. The LMIs allow the synthesis of one LTI controller, providing the required performance and system stability margin for each model from a given array. Tracking cascades use new MIMO PID controllers adjusted by means of the LMIs.