The paper is devoted to the design and simulation of a multivariable cascade system with a Hinf controller in the outer loop which has the goal to track plasma shape and current in a tokamak by manipulation of control current references. These currents flow in magnetic coils located around a tokamak vacuum vessel and generate a poloidal magnetic field to confine the high-temperature plasma inside the vessel. For the controller K design a mixed-sensitivity objective was achieved by minimization of the Hinf-norm of the stacked and shaped transfer function S/KS where the sensitivity S is a matrix transfer function from a plant external disturbance to plasma shape and current signals. The H¥ approach was applied in the outer cascade to the plant consisting of two inner loops of the system. The first scalar inner loop stabilizes a plasma unstable vertical position speed at about zero. The second inner multivariable loop was preliminary designed to decouple control currents. The cascade system was simulated with plasmaphysics DINA code in the divertor phase of the plasma current ramp-up stage for two scenarios: the ITER 15 MA scenario and another one with a new set of scenario control currents given by the control system from the initial simulation. The motivation of the H¥ outer loop design is to enhance the robust stability margin of the system in comparison with the known system consisting of the series connection of the pseudo-inverse matrix and diagonal PII-controller with a double integrator in the outer multivariable loop without losing tracking accuracy. The Hinf cascade control system showed about five times larger the robust stability margin estimated by means of singular values of the complementary sensitivity T in frequency domain.