DocumentCode :
863543
Title :
Convolution z -transform method applied to certain nonlinear discrete systems
Author :
Jury, E.I. ; Pai, M.A.
Author_Institution :
University of Pittsburgh, Pittsburgh, PA, USA
Volume :
7
Issue :
1
fYear :
1962
fDate :
1/1/1962 12:00:00 AM
Firstpage :
57
Lastpage :
64
Abstract :
This paper extends to discrete systems the method of complex convolution developed by Weber [6] for continuous systems. In this paper the convolution z -transform method is applied to obtain an explicit solution of certain nonlinear difference equations. The explicit solution is often desired for system design as well as for obtaining the response for large intervals of time. In these difference equations which describe the physical discrete systems, it is assumed that the nonlinearities are "small." This is necessitated by the form of solution applicable to the use of the convolution method. The advantage of the method is to systematize the procedure for the solution as well as to obtain results in a closed form. The convergence of the solution is discussed as well as applications to certain examples. Two numerical examples are worked out to illustrate the method. Explicit approximate solution is obtained and the results compare favorably with the numerical solution of the nonlinear difference equation as a recurrence relationship.
Keywords :
Closed-form solution; Convergence; Convolution; Difference equations; Differential equations; Helium; Laplace equations; Nonlinear equations; Research and development; Systems engineering and theory;
fLanguage :
English
Journal_Title :
Automatic Control, IRE Transactions on
Publisher :
ieee
ISSN :
0096-199X
Type :
jour
DOI :
10.1109/TAC.1962.1105405
Filename :
1105405
Link To Document :
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