ROBUSTNESS MEASURES FOR LINEAR-SYSTEMS WITH APPLICATION TO STABILITY RADII OF HURWITZ AND SCHUR POLYNOMIALS

In this paper we consider robustness measures (stability radii) for sy stem matrices which are subjected to structured real and complex pertu rbations of the form A BAR-arrow-pointing-right A + BDC where B, C are given matrices. Our object is twofold: (a) to present a number of new results, mainly concerning the real stability radius and its differen ces from the complex one; (b) to give an overview of our approach to t he robustness analysis of linear state space systems, including basic properties and characterizations of the complex stability radius. Appl ying the results to the special case where A is in companion form and B = [0, 0, ..., 0, 1]T, we are able to determine stability radii for H urwitz and Schur polynomials under arbitrary complex and real affine p erturbations of the coefficient vector. Computable formulae are obtain ed and illustrated by several examples.