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
Link To Document :
