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

Citation
D. Hinrichsen et Aj. Pritchard, ROBUSTNESS MEASURES FOR LINEAR-SYSTEMS WITH APPLICATION TO STABILITY RADII OF HURWITZ AND SCHUR POLYNOMIALS, International Journal of Control, 55(4), 1992, pp. 809-844
Citations number
47
ISSN journal
00207179
Volume
55
Issue
4
Year of publication
1992
Pages
809 - 844
Database
ISI
SICI code
0020-7179(1992)55:4<809:RMFLWA>2.0.ZU;2-R
Abstract
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.