Equation for loop bound in quantitative feedback theory

According to quantitative feedback theory, in the single-input single-output case, there exists at each frequency a lower bound for the nominal loop transmission function to satisfy the frequency-domain specification. It is proved that, in the complex plane, this lower bound is the boundary of a set of circles with centers and radii known. In the Nichols chart, the magnitude of the lower bound may not be a single-valued function of the phase.<>