A shaping limitation of rational sensitivity functions with a degree constraint

This note concerns a certain shaping limitation of sensitivity functions. The focus is on a frequency-wise infimum of gains of rational sensitivity functions with a degree constraint. An explicit infimum is derived for a special case. The result is useful for determining the inability of sensitivity functions of low degrees to achieve a specification in the frequency domain, and thus for motivating the use of higher degree sensitivity functions to fulfill the specification.