DocumentCode :
833511
Title :
On the Lyapunov matrix equation
Author :
Bialas, Stanislaw
Author_Institution :
Academy of Mining and Metallurgy, Krakow, Poland
Volume :
25
Issue :
4
fYear :
1980
fDate :
8/1/1980 12:00:00 AM
Firstpage :
813
Lastpage :
814
Abstract :
In this paper the inequality which is satisfied by the determinant of the solution of the Lyapunov matrix equation 
is presented. The result makes possible a lower estimate of product eigenvalues of the matrix 
and dependence from eigenvalues of the matrices 
and 
. This result corresponds to those presented in [2] and [3], where an estimate of the extremal eigenvalues of the matrix is presented. This estimate depends on the eigenvalues of the matrices and .
is presented. The result makes possible a lower estimate of product eigenvalues of the matrix and dependence from eigenvalues of the matrices and . This result corresponds to those presented in [2] and [3], where an estimate of the extremal eigenvalues of the matrix is presented. This estimate depends on the eigenvalues of the matrices and .Keywords :
Lyapunov matrix equations; Asymptotic stability; Constraint theory; Delay effects; Eigenvalues and eigenfunctions; Equations; Interconnected systems; Linear matrix inequalities; Lyapunov method; Sufficient conditions; Testing;
fLanguage :
English
Journal_Title :
Automatic Control, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9286
Type :
jour
DOI :
10.1109/TAC.1980.1102438
Filename :
1102438
Link To Document :
