DocumentCode
855462
Title
A counterexample for two conjectures about stability
Author
Demmel, James W.
Author_Institution
Courant Institute of Mathematics, New York, NY, USA
Volume
32
Issue
4
fYear
1987
fDate
4/1/1987 12:00:00 AM
Firstpage
340
Lastpage
342
Abstract
One measure of the stability of a matrix 
is the distance to the nearest unstable matrix 
. Recently Van Loan presented an algorithm to compute which depended on a conjecture about the location of its eigenvalues. We provide a counterexample to this conjecture which shows that the algorithm may overestimate the distance to by an arbitrary amount. The same counterexample invalidates another conjecture and algorithm of the author.
is the distance to the nearest unstable matrix . Recently Van Loan presented an algorithm to compute which depended on a conjecture about the location of its eigenvalues. We provide a counterexample to this conjecture which shows that the algorithm may overestimate the distance to by an arbitrary amount. The same counterexample invalidates another conjecture and algorithm of the author.Keywords
Eigenvalues/eigenvectors; Matrices; Stability; Circuit stability; Circuit synthesis; Design methodology; Eigenvalues and eigenfunctions; Feedback; Nonlinear dynamical systems; Robust stability; Robustness; Sufficient conditions; System analysis and design;
fLanguage
English
Journal_Title
Automatic Control, IEEE Transactions on
Publisher
ieee
ISSN
0018-9286
Type
jour
DOI
10.1109/TAC.1987.1104595
Filename
1104595
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