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

Kazuo KOMATSU; Hitoshi TAKATA; Teruo TSUJI

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

Kazuo KOMATSU, Hitoshi TAKATA, Teruo TSUJI

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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.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E77-A No.11 pp.1753-1757

Publication Date: 1994/11/25

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Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and Its Applications)

Category: Analysis of Nonlinear Circuits and Systems

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Kazuo KOMATSU, Hitoshi TAKATA, Teruo TSUJI, "A Formal Linearization of Nonlinear Systems by the Chebyshev Interpolation and a Nonlinear Filter as an Application" in IEICE TRANSACTIONS on Fundamentals, vol. E77-A, no. 11, pp. 1753-1757, November 1994, doi: .
Abstract: 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e77-a_11_1753/_p

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@ARTICLE{e77-a_11_1753,
author={Kazuo KOMATSU, Hitoshi TAKATA, Teruo TSUJI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Formal Linearization of Nonlinear Systems by the Chebyshev Interpolation and a Nonlinear Filter as an Application},
year={1994},
volume={E77-A},
number={11},
pages={1753-1757},
abstract={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.},
keywords={},
doi={},
ISSN={},
month={November},}

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TY - JOUR
TI - A Formal Linearization of Nonlinear Systems by the Chebyshev Interpolation and a Nonlinear Filter as an Application
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1753
EP - 1757
AU - Kazuo KOMATSU
AU - Hitoshi TAKATA
AU - Teruo TSUJI
PY - 1994
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E77-A
IS - 11
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - November 1994
AB - 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.
ER -