RESEARCH PAPERS: Papers on Bilinear Control

Volterra Series Expansion for Bilinear Systems in a Nonlinear Feedback Loop

[+] Author and Article Information
A. Bertuzzi

Istituto di Analisi dei Sistemi ed Informatica del CNR, Rome, Italy

C. Bruni

Istituto di Automatica, Facolta di Ingegneria del l’Universita di Roma, Rome, Italy 00184

A. Gandolfi, A. Germani

Istituto di Analisi dei Sestemi ed Informatica del CNR, Rome, Italy

J. Dyn. Sys., Meas., Control 103(2), 84-88 (Jun 01, 1981) (5 pages) doi:10.1115/1.3139659 History: Received April 08, 1980; Online July 21, 2009


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.

Copyright © 1981 by ASME
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