Theory of pth-order inverses of nonlinear systems

Author

Schetzen, Martin

Volume

Issue

fYear

1976

fDate

5/1/1976 12:00:00 AM

Firstpage

285

Lastpage

291

Abstract

The concept and theory of the $p$ th-order inverse of a nonlinear system es developed in this article. The $p$ th-order inverse, $K_{(p)}^{-1}$ , of a system $H$ is defined as a system for which the Volterra series of the system $Q$ formed by the tandem connection of $K_{(p)}^{-1}$ and $H$ is $Q[x]= x+ \\Sigma _{n=p+1}^{\\infty } Q_{n}[x]$ so that the 2nd through the $p$ th-order Volterra operators of $Q$ are zero. The necessary and sufficient conditions for the existence of $K_{(p)}^{-1}$ are determined. It is shown that the $p$ th-order pre-inverse of a system $H$ is identical to its $p$ th-order post-inverse. In addition, a synthesis of $K_{(p)}^{-1}$ is obtained. The $p$ th-order inverse offers an approach to the study of the system inverse, $H^{-1}$ , since, as $p \\rightarrow \\infty , K_{(p)}^{-1}$ becomes the Volterra series of $H^{-1}$ . 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

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1177647