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A computer method for formal linearization of nonlinear systems by the discrete fourier expansion and its applications
Author(s) -
Komatsu Kazuo,
Takata Hitoshi,
Tsuji Teruo
Publication year - 1995
Publication title -
electrical engineering in japan
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.136
H-Index - 28
eISSN - 1520-6416
pISSN - 0424-7760
DOI - 10.1002/eej.4391150408
Subject(s) - linearization , nonlinear system , fourier series , mathematics , feedback linearization , trigonometric polynomial , trigonometric functions , split step method , fourier transform , trigonometric integral , control theory (sociology) , fourier analysis , mathematical analysis , differential equation , trigonometry , computer science , physics , geometry , control (management) , quantum mechanics , artificial intelligence
This paper proposes a numerical computer method for formal linearization of 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 trigonometric functions. The nonlinear terms of the differential equations are expanded into finite sums of trigonometric functions by the method of the discrete Fourier expansion. As a result, a formal linear system is derived from the given nonlinear system. A computer algorithm of the linearization is acquired and numerical computation is easily carried out with the aid of computers. Further, as the application of the linearization, both a nonlinear observer and a nonlinear filter are synthesized in this paper. Examples show that the accuracy of the method is improved as the order of the trigonometric functions increases.