The paper presents the design and simulation results of the combined multivariable control system with the plant input constraints for a plasma current profile in a tokamak. The plasma kinetic model was used in terms of the Grad-Shafranov plasma equilibrium equation and the poloidal magnetic flux diffusion equation. The model is square specifically contains 5 inputs and 5 outputs. Actuators are external current drive sources. Output is plasma current density measured at five points of the minor radius. A set of linear models for controller design was obtained by a state subspace identification approach. A set of H∞ controllers was synthesized by a loop shaping methodology at various values of the plasma electron temperature on the magnetic axis. Controllers designed were applied by the numerical simulation to the original model to change the current profile from one state to another. In the presence of plant input constraints a special logic block was developed in addition to the linear robust controller and used when plant inputs saturated. The plasma current profile control system designed showed its operability in the tokamak plasma electron temperature range on the magnetic axis from 0.1 to 18 keV.