Robustness measures for linear systems with application to stability radii of Hurwitz and Schur polynomials

Abstract

In this paper we consider robustness measures (stability radii) for system matrices which are subjected to structured real and complex perturbations of the form A↦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 differences from the complex one; (b) to give an overview of our approach to the robustness analysis of linear state space systems, including basic properties and characterizations of the complex stability radius. Applying 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 Hurwitz and Schur polynomials under arbitrary complex and real affine perturbations of the coefficient vector. Computable formulae are obtained and illustrated by several examples