A Geometric Representation of Root Sensitivity

Abstract

In this paper, we present a geometric method for representing the classical root sensitivity function of linear time-invariant dynamic systems. The method employs specialized eigenvalue plots that expand the information presented in the root locus plot in a manner that permits determination by inspection of both the real and imaginary components of the root sensitivity function. We observe relationships between root sensitivity and eigenvalue geometry that do not appear to be reported in the literature and hold important implications for control system design and analysis.