The decentralised design of robust damping controllers is presented based on the linear matrix inequality (LMI) approach employing several superconducting magnetic energy storage (SMES) devices. These controllers are aimed at enhancing the damping of multiple inter-area modes in a large power system. The paper describes a comprehensive and systematic way of designing these controllers. Eigenvalue technique and nonlinear simulations further verify the robustness of the damping controllers for various operating conditions and load characteristics.