A Formal Linearization of Nonlinear Systems by the Chebyshev Interpolation and a Nonlinear Filter as an Application

Kazuo KOMATSU  Hitoshi TAKATA  Teruo TSUJI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E77-A   No.11   pp.1753-1757
Publication Date: 1994/11/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and Its Applications)
Category: Analysis of Nonlinear Circuits and Systems
formal linearization,  nonlinear systems,  nonlinear filter,  Chebyshev interpolation,  

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In this paper we propose a formal linearization method which permits us to transform nonlinear systems into linear systems by means of the Chebyshev interpolation. Nonlinear systems are usually represented by nonlinear differential equations. We introduce a linearizing function that consists of a sequence of the Chebyshev polynomials. The nonlinear equations are approximated by the method of Chebyshev interpolation and linearized with respect to the linearizing function. The excellent characteristics of this method are as follows: high accuracy of the approximation, convenient design, simple operation, easy usage of computer, etc. The coefficients of the resulting linear system are obtained by recurrence formula. The paper also have error bounds of this linearization which show that the accuracy of the approximation by the linearization increases as the order of the Chebyshev polynomials increases. A nonlinear filter is synthesized as an application of this method. Numerical computer experiments show that the proposed method is able to linearize a given nonlinear system properly.