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
Link To Document :
