A computation method of formal linearization for time-variant nonlinear systems via Chebyshev interpolation

We consider a computer method of transforming time-variant nonlinear systems into time-variant linear ones. Introducing a linearizing function which consists of the Chebyshev polynomials, the nonlinear time-variant systems are transformed into linear time-variant systems with respect to these linearizing functions using the Chebyshev interpolation. Error bounds of this formal linearization are also discussed in this paper, which shows that the accuracy of the approximation by the linearization improves as the order of the Chebyshev polynomials increases. Nonlinear observer and filter are synthesized for time-variant systems as applications of this linearization. Numerical experiments are included to show the high validity of this formal linearization.