Exponential describing function in the analysis of nonlinear systems

Author

Bickart, Theodore A.

Author_Institution

Syracuse University, Syracuse, NY, USA

Volume

11

Issue

3

fYear

1966

fDate

7/1/1966 12:00:00 AM

Firstpage

491

Lastpage

497

Abstract

In this paper, signals in $(L)_{2}(- \\infty , t]$ , a subspace of the space of square integrable signals defined on $(- \\infty , t]$ , are approximated by signals in $(L)_{2}^{1}(- \\infty , t]$ , the one-dimensional subspace of $(L)_{2}(- \\infty , t]$ spanned by the first function from the set of reversed time Laguerre functions. A system mapping $(L)_{2}(- \\infty , t]$ into itself is associated with a system mapping $(L)_{2}^{1}(- \\infty t]$ into itself; the latter system is characterized by a gain-exponential describing function. This type of describing function is developed as an analysis tool for studying the transient response of a large class of nonlinear feedback systems. The contraction-mapping fixed-point theorem is used to develop conditions for the existence of a solution prior to the use of the exponential describing function to obtain an approximate solution.

Keywords

Describing functions; Nonlinear systems; Circuit theory; Control systems; Feedback; Helium; Nonlinear control systems; Nonlinear systems; Regulators; Signal analysis; Transient analysis; Transient response;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.1966.1098379

Filename

1098379