Robust stability and eigenvectors of uncertain matrices

Author

Wang, Sheng-Guo ; Lin, Shield B.

Author_Institution

Dept. of Mech. Eng., Prairie View A&M Univ., TX, USA

Volume

3

fYear

1995

fDate

21-23 Jun 1995

Firstpage

2399

Abstract

This paper presents the relationship between eigenvectors and Hurwitz stability of uncertain matrices. First, it reveals new necessary and sufficient conditions for stability of a nominal matrix A through the relationship of its eigenvectors and its symmetric criterion matrices. Three types of criterion matrices are adopted, i.e., the direct symmetric matrix A_s=(A+A*)/2, the similarity transformed symmetric matrix and the Lyapunov-type symmetric matrix. Then, the necessary and sufficient conditions for robust stability of uncertain matrices are provided by using their eigenvector directions with respect to a basis constituted by their symmetric criterion matrix eigenvectors. The concerned uncertainties include both structured and unstructured uncertainties. The results may be applied to control systems for robust stability analysis and design

Keywords

Lyapunov matrix equations; continuous time systems; eigenvalues and eigenfunctions; linear systems; robust control; uncertain systems; Hurwitz stability; Lyapunov-type symmetric matrix; direct symmetric matrix; dynamic uncertain systems; eigenvectors; linear continuous time systems; necessary condition; robust stability; similarity transformed symmetric matrix; sufficient conditions; symmetric criterion matrix; uncertain matrices; Books; Control systems; Mechanical engineering; Robust control; Robust stability; Stability criteria; Sufficient conditions; Symmetric matrices; Uncertain systems; Uncertainty;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference, Proceedings of the 1995

Conference_Location

Seattle, WA

Print_ISBN

0-7803-2445-5

Type

conf

DOI

10.1109/ACC.1995.531403

Filename

531403