In this paper, the problem of finding the set of Proportional Integral Derivative (PID) controllers that can robustly stabilize a system based on its frequency response has been solved. The model of the system is not necessary for this problem. A band of uncertainty is assumed in the frequency response of the plant. The controller is so designed that it can robustly stabilize this plant in the entire range of its uncertainties. Interval coefficient linear inequalities are used to arrive at the final result.
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