On a Pseudo-Formal Linearization Method Based on Fourier Series Expansion

This paper is concerned with a pseudo-formal linearization method using the Fourier series expansion. The given nonlinear dynamic system is piecewisely linearized into some augmented linear systems with respect to a linearization function that consists of the state variables and their trigonometric functions. The resulting linear systems are smoothly united into a single system. Its application to a nonlinear observer and numerical examples are also included.