This paper deals with the H∞ stabilization of the spatial distribution of the current profile of tokamak plasmas using a Linear Matrix Inequality (LMI) approach. The control design is based on the one dimensional resistive diffusion equation of the magnetic flux that governs the plasma current profile evolution. The feedback control law is derived in the infinite dimensional setting without spatial discretization. The proposed distributed control is based on a proportional–integral state feedback taking into account both interior and boundary engineering actuators. Supporting numerical simulations are presented and tuning of the controller parameters attenuating uncertain disturbances is discussed.