The extreme eigenvalues and stability of real symmetric interval matrices
- 1 April 1992
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 37 (4) , 532-535
- https://doi.org/10.1109/9.126593
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
This publication has 1 reference indexed in Scilit:
- Necessary and sufficient conditions for stability of symmetric interval matricesInternational Journal of Control, 1990