Combinatorial Approximations of Volterra Series by Bilinear Systems

1991 ◽  
pp. 304-315 ◽  
Author(s):  
Françoise Lamnabhi-Lagarrigue ◽  
Pierre Leroux ◽  
Xavier G. Viennot
Keyword(s):  
Volterra Series ◽  
Bilinear Systems

Volterra Series Expansion for Bilinear Systems in a Nonlinear Feedback Loop

1981 ◽  
Vol 103 (2) ◽  
pp. 84-88
Author(s):  
A. Bertuzzi ◽  
C. Bruni ◽  
A. Gandolfi ◽  
A. Germani
Keyword(s):  
Series Expansion ◽  
Existence And Uniqueness ◽  
Feedback Loop ◽  
Volterra Series ◽  
Approximation Theorem ◽  
Bilinear Systems ◽  
Nonlinear Feedback ◽  
Input Output ◽  
Distributed Bilinear Systems ◽  
Weierstrass Approximation Theorem

In this paper the class of distributed bilinear systems in a nonlinear feedback loop is considered. First of all the existence and uniqueness of solution is stated when input and state belong to L2 spaces. Then the existence of the Volterra series expansion for the input-output map is proved for inputs in any sphere around the origin; the proof is based on a new version of the Weierstrass approximation theorem.

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