The extreme eigenvalues and stability of real symmetric interval matrices

Author

Hertz, David

Author_Institution

Rafael, Haifa, Israel

Volume

37

Issue

4

fYear

1992

fDate

4/1/1992 12:00:00 AM

Firstpage

532

Lastpage

535

Abstract

A novel Khoritonov-like algorithm for computing the minimal and maximal eigenvalues of n*n dimensional symmetric interval matrices is presented. It is proved that the maximal eigenvalue of a given set of interval matrices coincides with the maximal eigenvalue of a special set of 2/sup n-1/ symmetric vertex matrices, whereas its minimal eigenvalue coincides with the minimal of another special set of 2/sup n-1/ symmetric vertex matrices. As immediate corollaries of this algorithm, weak necessary and sufficient conditions for testing the Hurwitz and Schur stability of symmetric interval matrices, where one has to test the stability of 2/sup n-1/ and 2/sup n/ symmetric vertex matrices, respectively, are obtained.<>

Keywords

eigenvalues and eigenfunctions; matrix algebra; stability; 2/sup n-1/ symmetric vertex matrices; 2/sup n/ symmetric vertex matrices; Hurwitz stability; Khoritonov-like algorithm; Schur stability; extreme eigenvalues; maximal eigenvalues; minimal eigenvalue; real symmetric interval matrices; stability; weak necessary and sufficient conditions; Clustering algorithms; Computational modeling; Eigenvalues and eigenfunctions; Robustness; Stability; Sufficient conditions; Symmetric matrices; Testing;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.126593

Filename

126593