DocumentCode :
1177647
Title :
Theory of pth-order inverses of nonlinear systems
Author :
Schetzen, Martin
Volume :
23
Issue :
5
fYear :
1976
fDate :
5/1/1976 12:00:00 AM
Firstpage :
285
Lastpage :
291
Abstract :
The concept and theory of the 
th-order inverse of a nonlinear system es developed in this article. The th-order inverse, 
, of a system 
is defined as a system for which the Volterra series of the system 
formed by the tandem connection of and is ![Q[x]= x+ \\Sigma _{n=p+1}^{\\infty } Q_{n}[x]](/images/tex/10326.gif)
so that the 2nd through the th-order Volterra operators of are zero. The necessary and sufficient conditions for the existence of are determined. It is shown that the th-order pre-inverse of a system is identical to its th-order post-inverse. In addition, a synthesis of is obtained. The th-order inverse offers an approach to the study of the system inverse, 
, since, as 
becomes the Volterra series of . This approach is discussed and some applications with regard to nonlinear differential equations and nonlinear feedback systems are presented.
th-order inverse of a nonlinear system es developed in this article. The th-order inverse, , of a system is defined as a system for which the Volterra series of the system formed by the tandem connection of and is so that the 2nd through the th-order Volterra operators of are zero. The necessary and sufficient conditions for the existence of are determined. It is shown that the th-order pre-inverse of a system is identical to its th-order post-inverse. In addition, a synthesis of is obtained. The th-order inverse offers an approach to the study of the system inverse, , since, as becomes the Volterra series of . This approach is discussed and some applications with regard to nonlinear differential equations and nonlinear feedback systems are presented.Keywords :
Inverse systems; Nonlinear circuits and systems; Nonlinear systems, continuous-time; Volterra series; Circuits and systems; Differential equations; Feedback; Helium; Kernel; Linear systems; Nonlinear systems; Sufficient conditions;
fLanguage :
English
Journal_Title :
Circuits and Systems, IEEE Transactions on
Publisher :
ieee
ISSN :
0098-4094
Type :
jour
DOI :
10.1109/TCS.1976.1084219
Filename :
1084219
Link To Document :
