DocumentCode
837289
Title
Eigenvalue bounds in the Lyapunov and Riccati matrix equations
Author
Nicholson, David W.
Author_Institution
Naval Surface Weapons Center, White Oak, Silver Spring, MD, USA
Volume
26
Issue
6
fYear
1981
fDate
12/1/1981 12:00:00 AM
Firstpage
1290
Lastpage
1291
Abstract
Two related theorems of Strang [1] are extended to provide upper and lower bounds on the eigenvalues of the Lyapunov and Riccati matrices, given by 
and 
, where 
and 
are Hermitian, positive definite, complex matrices. We discuss inversion to obtain eigenvalue bounds on the matrix for the usual case in which 
, and are known.
and , where and are Hermitian, positive definite, complex matrices. We discuss inversion to obtain eigenvalue bounds on the matrix for the usual case in which , and are known.Keywords
Algebraic Riccati equation (ARE); Eigenvalues/eigenvectors; Lyapunov matrix equations; Riccati equations, algebraic; Eigenvalues and eigenfunctions; Explosions; Linear matrix inequalities; Mercury (metals); Protection; Riccati equations; Silver; Springs; US Government; Weapons;
fLanguage
English
Journal_Title
Automatic Control, IEEE Transactions on
Publisher
ieee
ISSN
0018-9286
Type
jour
DOI
10.1109/TAC.1981.1102809
Filename
1102809
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