Singular-value and eigenvalue techniques in the analysis of systems with structured perturbations

Abstract

A new range of techniques is introduced for the purpose of exploiting information about the structure of the perturbation associated with uncertain linear multi-variable feedback systems. The class of perturbation considered is wide and ignores only the phase information of the individual elements of the perturbation matrix; it encompasses diagonal, block-diagonal and other forms of block-structured perturbations. The techniques developed provide a means of assessing stability margins and also lead to an extension of the Nyquist criterion.