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Centralized control using system-wide data has been suggested to enhance the dynamic performance of large interconnected power systems. Because of the distance involved in wide-area interconnections, communication delay cannot be ignored. Long time delay may be detrimental to system stability and may degrade system performance. The time delay tolerance of a centralized controller and the associated performance tradeoff is analyzed using a small gain criterion. Special attention is paid to the choice of weighting functions in a robust control design. As expected, it is found that time delay tolerance decreases when the system bandwidth increases, while the nominal system time-domain performance is concomitantly improved. Several approaches which can maintain a good system performance while increasing the time delay tolerance are suggested and compared. A modern controller design technique, like gain scheduling via linear matrix inequalities, is evaluated for the design of the supervisory power system stabilizer accounting for various time delays.