Modern power networks are enormously complex and frequently interconnected by weak tie-lines, which results in a variety of stability issues such as low frequency oscillations (LFOs). LFOs can have a negative impact on power system stability and tie-line transmission capacity, resulting in catastrophic blackouts if suitable damping control mechanisms are not in situ. This article demonstrates a robust design of damping control for inter-area LFO damping in an interconnected power system. A new comprehensive approach is presented, which integrates the thyristor controlled series compensator (TCSC) and superconducting magnetic energy storage (SMES) to improve the damping of critical inter-area modes. An intelligently designed fuzzy logic control (FLC) employing a global stabilizing feedback signal constitutes the supervisory controller. The stabilizing feedback signal is obtained based on the observability of critical modes using participation factor (PF) analysis. Moreover, a maiden application of a recently proposed optimization algorithm, Kmeans optimizer (KO), is employed to simultaneously tune the parameters of FLC employed for coordinated operation of SMES and TCSC. To validate the robustness of the proposed scheme, several case studies are performed on Kundur's two-area multi-machine test system. A comparison with a residuebased damping controller was also done to demonstrate the superior damping efficacy of the proposed KOFLC controller.