| Abstract: | 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. |
