DocumentCode :
827914
Title :
The existence and uniqueness of Volterra series for nonlinear systems
Author :
Lesiak, Casimir ; Krener, Arthur J.
Author_Institution :
University of California, Davis, CA, USA
Volume :
23
Issue :
6
fYear :
1978
fDate :
12/1/1978 12:00:00 AM
Firstpage :
1090
Lastpage :
1095
Abstract :
Given an input-output map described by a nonlinear control system \\dot{x}=f(x,u) and nonlinear output y=h(x) , we present a simple straightforward means for obtaining a series representation of the output y(t) in terms of the input u(t) . When the control enters linearly, \\dot{x} =f(x)+ ug(x) , the method yields the existence of a Volterra series representation. The proof is constructive and explicitly exhibits the kernels. It depends on standard mathematical tools such as the Fundamental Theorem of Calculus and the Cauchy estimates for the Taylor series coefficients of analytic functions. In addition, the uniqueness of Volterra series representations is discussed.
Keywords :
Bilinear systems, continuous-time; Nonlinear systems, continuous-time; Volterra series; Control systems; Differential equations; Kernel; Linear systems; Mathematics; Nonlinear control systems; Nonlinear systems; Stability; Taylor series;
fLanguage :
English
Journal_Title :
Automatic Control, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9286
Type :
jour
DOI :
10.1109/TAC.1978.1101898
Filename :
1101898
Link To Document :
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