DocumentCode :
804685
Title :
On spectral mappings, higher order circle criteria, and periodically varying systems
Author :
Zames, G. ; Kallman, R.R.
Author_Institution :
Department of Transportation, Cambridge, MA, USA
Volume :
15
Issue :
6
fYear :
1970
fDate :
12/1/1970 12:00:00 AM
Firstpage :
649
Lastpage :
652
Abstract :
For feedback equations of the form e = x - He , in which H is a linear operator, stability boundaries obtained by the circle criterion method can frequently be improved by finding a function f(H) which conformally maps the spectrum of H from its initial region in the complex plane into a more suitable region. This idea, which is based on the spectral mapping theorem of Banach algebras, is applied here to a class of equations consisting of a time-invariant part and a periodically time-varying gain. A stability bound is derived which has a minimum whenever the frequency response of the time-invariant part peaks at a frequency near one half that of the time-varying gain.
Keywords :
Linear systems; Nonlinear systems; Algebra; Asymptotic stability; Feedback; Integral equations; Nonlinear equations; Nonlinear systems; Stability criteria; Sufficient conditions; Time varying systems; Transportation;
fLanguage :
English
Journal_Title :
Automatic Control, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9286
Type :
jour
DOI :
10.1109/TAC.1970.1099587
Filename :
1099587
Link To Document :
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