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The attainment of diagonal dominance in an inverse Nyquist array of 2-variable control systems is examined for constant matrix compensation placed in the forward path. A quadratic inequality is obtained from Gershgorin's inequality, and this leads directly to a simple graphical-design technique for achieving row diagonal dominance. A useful outcome of the method is that it reveals cases in which solutions of this form do not exist. Alternatively, when row dominance can be satisfied, the complete set of solutions is obtained.