This paper presents an H« controller synthesised based on linear matrix inequalities (LMI) for a current source converter based superconducting magnetic energy systems (SMESs) connected to a node of power systems where the regulation of grid current has considered as a control objective. To facilitate the control design, the system is represented in terms of state space realization with uncertainties. The control design involves selecting proper weighting functions and performing LMI-synthesis. The controller order is reduced by Henkel-norm method. Simulations are carried out to evaluate the characteristics of the controller under parametric uncertainties. It is found out that the proposed controller is inherently stable, possesses significantly small tracking error, and preserves robust performance for the SMES.