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This paper presents a novel approach to damp interarea oscillations by designing a robust multi-input multioutput supplementary controller for multiterminal dc (MTDC) systems embedded in ac grids. The key idea to achieve robustness lies in explicitly modeling the MTDC current injection as disturbances using an \mathcal H\infty mixed-sensitivity formulation in the linear matrix inequality framework. Control directions are established by selecting wide-area feedback signals and the relative gain array computation. Robustness is assessed through dynamic simulations for scenarios including: first, disturbances on the ac side, second, disturbances on the dc-side such as loss of a converter pole including actuator, third, partial loss of feedback signal, and fourth, communication latencies. The performance of the proposed controller is compared against the conventional \mathcal H\infty based design, using a four-terminal dc grid embedded within the New England–New York test system. The results suggest that the proposed approach demonstrates superior performance following dc-side disturbances, actuator outages, and latency. [ABSTRACT FROM PUBLISHER]