Abstract
This paper is concerned with a pseudo-formal linearization method using Chebyshev expansion and its application to a nonlinear observer for nonlinear scalar-measurement systems. The given nonlinear autonomous dynamic system is linearized into an augmented linear system with respect to a linearization function that consists of polynomials of state variables by a pseudo-formal linearization method using Chebyshev expansion. As an application of this method, a nonlinear observer is discussed. An augmented measurement vector that consists of polynomials of measurement data is introduced and is transformed into an augmented linear one by the pseudo-formal linearization technique using Chebyshev expansion. Thereby, a linear system theory is applied to both the linearized dynamic and measurement systems in order to design a new nonlinear observer. Numerical experiments indicate that the performance of the presented method is superior to that of the previous method.
