DocumentCode :
863959
Title :
Verification of Aizerman´s conjecture for a class of third-order systems
Author :
Bergen, A.R. ; Williams, I.J.
Author_Institution :
University of California, Berkeley, CA, USA
Volume :
7
Issue :
3
fYear :
1962
fDate :
4/1/1962 12:00:00 AM
Firstpage :
42
Lastpage :
46
Abstract :
The second method of Lyapunov is used to validate Aizerman\´s conjecture for the class of third-order nonlinear control systems described by the following differential equation: 
In this case, the stability of the nonlinear system may be inferred by considering an associated linear system in which the nonlinear function 
is replaced by 
. If the linear system is asymptotically stable for 
, then the nonlinear system will be asymptotically stable in-the-large for any for which 
The Lyapunov function used to prove this result is determined in a straightforward manner by considering the physical behavior of the system at the extreme points of the allowable range of 
.
In this case, the stability of the nonlinear system may be inferred by considering an associated linear system in which the nonlinear function is replaced by . If the linear system is asymptotically stable for , then the nonlinear system will be asymptotically stable in-the-large for any for which The Lyapunov function used to prove this result is determined in a straightforward manner by considering the physical behavior of the system at the extreme points of the allowable range of .Keywords :
Differential equations; Gain; Linear systems; Lyapunov method; Nonlinear control systems; Nonlinear systems; Poles and zeros; Regulators; Research and development; Stability analysis;
fLanguage :
English
Journal_Title :
Automatic Control, IRE Transactions on
Publisher :
ieee
ISSN :
0096-199X
Type :
jour
DOI :
10.1109/TAC.1962.1105447
Filename :
1105447
Link To Document :
