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In this paper, we develop a new damping control scheme for FACTS devices, using bang-bang modulation of FACTS signals. The scheme is used to attenuate quickly the system's most dominant mode which is identified using online Prony analysis. An analysis framework to evaluate the robustness of the control schemes to changes in operating conditions and to time-delay is also proposed. Simulation results on various test systems show that following large disturbances, the proposed control scheme is very effective to mitigate the power system critical modes of oscillation. Furthermore, the problem of control interactions is completely avoided with the proposed control scheme.