A hybrid AC/DC microgrid is established with the aim of exploiting numerous types of renewable energy to meet the needs of different loads. The microgrid is decomposed by AC DC sub-grids which are connected by an interlink converter (IC). To maintain the security and reliability of the microgrid, an automatic controller for the interlink converter is needed. In this paper, we propose a Linear Matrix Inequalities (LMI)-based current control method for the interlink converter. As the main features here, the interlink converter permits bidirectional power exchange between both sub-grids when a power-demand imbalance occurs in one sub-grid regardless of the converter system parameters. Simulations with various filter parameters are performed using the Matlab/Simulink software to validate the effectiveness of the proposed controller. In comparison with the existing Linear Quadratic Regulator (LQR)-based current control, the proposed method is more robust against unknown system parameters and high load perturbation.