A Computer Method of the Formal Linearization for Nonlinear Systems by the Discrete Fourier Expansion and Its Applications

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  • 離散フーリエ展開による非線形システムの形式的線形化計算法とその応用
  • リサン フーリエ テンカイ ニ ヨル ヒセンケイ システム ノ ケイシキテキ

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In this paper we propose a numerical computer method of the formal linearization for nonlinear systems by using the discrete Fourier expansion. A nonlinear system is described by a system of nonlinear ordinary differential equations. A linearizing function is given by a sequence of the trigonometric functions. The nonlinear terms of the differential equations are expanded into finite sums of the trigonometric functions by the method of the discrete Fourier expansion. As a result, a formal linear system is derived from the given nonlinear system.<br>A computer algorithm of the linearization is acquired and numerical computation is easily carried out with the aid of computers. Besides, as the application of the linearization, both a nonlinear observer and a nonlinear filter are also synthesized in the paper. Examples show that the accuracy of the method is improved as the order of the trigonometric functions increases.

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