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The paper presents a robust probabilistic methodology for assessing the performance of power system controllers. In this study, the proposed probabilistic technique is applied to a novel power oscillation damping (POD) controller structure implemented through active power modulation of multiple voltage source converter based high voltage direct current (VSC-HVDC) links within a large heavily meshed network exhibiting multiple inter-area modes. The modal linear quadratic Gaussian (MLQG) controller, as an example of advanced POD, is implemented in both a centralized and a decentralized form for comparison. Following the development and demonstration of the effectiveness of the controller designs, the robust probabilistic performance evaluation is carried out incorporating outage contingencies for generators, lines, and VSC-HVDC lines. The results obtained demonstrate that both controller structures are largely robust to wide ranging operating conditions. For those conditions where controller performance is unsatisfactory, various mitigation techniques are discussed, including the use of classification tools to guide operational limits. A contingency specific controller design is shown to significantly improve performance when robustness cannot be achieved.