DocumentCode :
810719
Title :
A graphical test for checking the stability of a linear time-invariant feedback system
Author :
Callier, Frank M. ; Desoer, Charles A.
Author_Institution :
University of California, Berkeley, CA, USA and Belgian National Fund for Scientific Research, Brussels, Belgium
Volume :
17
Issue :
6
fYear :
1972
fDate :
12/1/1972 12:00:00 AM
Firstpage :
773
Lastpage :
780
Abstract :
A graphical test is developed for checking the condition 
where 
is a nonzero real constant and 
is the sum of a finite number of right-half plane poles and the Laplace transform of an integrable function plus a series of delayed impulses. As a conseqence, 
is, in 
, asymptotic to an almost periodic function, say 
, for 
. Theorem 1 gives a necessary and sufficient condition involving the curve 
to ensure that 
; Corollary 1 gives a corresponding graphical test. Theorem 2 and Corollary 2 give a necessary and sufficient condition involving the curve 
and a graphical test to ensure 
, a condition that guarantees the Lpstability of the feedback system for any ![p in [1,\\infty ]](/images/tex/3735.gif)
.
where is a nonzero real constant and is the sum of a finite number of right-half plane poles and the Laplace transform of an integrable function plus a series of delayed impulses. As a conseqence, is, in , asymptotic to an almost periodic function, say , for . Theorem 1 gives a necessary and sufficient condition involving the curve to ensure that ; Corollary 1 gives a corresponding graphical test. Theorem 2 and Corollary 2 give a necessary and sufficient condition involving the curve and a graphical test to ensure , a condition that guarantees the Lpstability of the feedback system for any .Keywords :
Linear systems, time-invariant continuous-time; Stability; Algebra; Convolution; Delay; Feedback; Impulse testing; Laboratories; Laplace equations; Stability; System testing; Transfer functions;
fLanguage :
English
Journal_Title :
Automatic Control, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9286
Type :
jour
DOI :
10.1109/TAC.1972.1100180
Filename :
1100180
Link To Document :
