Sensitivity reduction over a frequency band

Abstract

The problem of reducing the sensitivity of a possibly infinite-dimensional linear single-input single-output system over a finite frequency interval by feedback is considered. Specifically, the following are proven: (i) if one wants to bound the overall sensitivity, the existence of a non-trivial inner part inhibits the reduction of the sensitivity over the interval; (ii) in a system that is continuous and has at most countably many zeros on the imaginary axis, one can reduce the sensitivity over an interval to be arbitrarily small, while the overall sensitivity is kept bounded if and only if the system is outer and has no zeros on the interval. These extend results for rational transfer functions.