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Approximation of Nonlinear Systems by Bilinear Ones

  • C. Hespel
  • G. Jacob
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 29)

Abstract

Given an analytic system, we compute a bilinear system of minimal dimension which approximates it up to order k (i.e. the outputs of these two systems have the same Taylor expansion up to order k).

For that purpose, we use a noncommutative formal power series called the generating series of the system. Let s be the series, and y the output of the analytic system: we notice that the Taylor expansion of y up to order k in t=0 can be obtained from the coefficients of the words of length not greater than k in the series s. As rational series are characteristic of finite dimensional bilinear systems, the problem is reduced to the following: build a rational series g, which is an approximation of s up to order k (i.e. the coefficients of the words of length not greater than k in g and s are identical), and which is of minimal rank. Then with g we associate a bilinear system, which is a solution to our problem.

Keywords

Taylor Expansion Rational Series Generate Series Bilinear System Volterra Series 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© D. Reidel Publishing Company 1986

Authors and Affiliations

  • C. Hespel
    • 1
  • G. Jacob
    • 2
  1. 1.I.N.S.ARennes CedexFrance
  2. 2.Laboratoire de Recherche en Informatique Fondamentale (LA 369)Université de Lille IVilleneuve D’Ascq CedexFrance

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