DocumentCode :
854781
Title :
Two singular value inequalities and their implications in H∞ approach to control system design
Author :
Foo, Yung Kuan
Author_Institution :
Nanyang Technological Institute, Singapore, Republic of Singapore
Volume :
32
Issue :
2
fYear :
1987
fDate :
2/1/1987 12:00:00 AM
Firstpage :
156
Lastpage :
157
Abstract :
In this note we prove that if 
and 
are both nonnegative definite Hermitian matrices and 
is also nonnegative definite, then the singular values of A and B satisfy the inequalities 
, where 
denote the singular values of a matrix. A consequence of this property is that, in a nonsquare H^{infty} optimization problem, if ![\\sup_{\\omega } \\bar{\\sigma }[Z(j\\sigma )] {\\underline {\\underline \\Delta }} \\sup_{\\omega } \\bar{\\sigma }[x(j\\omega )^{T}/ Y(j\\omega )^{T}]^{T} = \\lambda](/images/tex/3311.gif)
, then the singular values of 
and 
satisfy the inequality ![\\lambda ^{2} \\geq \\max _{i} \\sup_{\\omega } [\\sigma _{i}^{2}(X) + \\sigma _{m-i-1}^{2}(Y)]](/images/tex/3312.gif)
where 
is the number of columns of the matrix 
.
and are both nonnegative definite Hermitian matrices and is also nonnegative definite, then the singular values of A and B satisfy the inequalities , where denote the singular values of a matrix. A consequence of this property is that, in a nonsquare H^{infty} optimization problem, if , then the singular values of and satisfy the inequality where is the number of columns of the matrix .Keywords :
H∞ optimization; Linear systems; Minimax control, linear systems; Control systems; Frequency; Functional analysis; Linear matrix inequalities; Minimax techniques; Transfer functions;
fLanguage :
English
Journal_Title :
Automatic Control, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9286
Type :
jour
DOI :
10.1109/TAC.1987.1104529
Filename :
1104529
Link To Document :
