A Pseudo-Formal Linearization for Nonlinear Time-Varying Systems via Chebyshev Expansion and Nonlinear Observer

This paper is concerned with a pseudo-formal linearization for nonlinear time-varying systems exploiting Chebyshev expansion, and a nonlinear observer design as an application of this method. A given nonlinear time-varying system can be transformed into several augmented linear time-varying systems by a pseudo-formal linearization based on Chebyshev expansion. And then we unite them into a single linear time-varying system by an automatic choosing function. As an application of the method, a nonlinear observer is synthesized. Numerical experiments show the effectiveness of the method.