On a Pseudo-Formal Linearization Method via the Orthogonal Polynomial Approximation

Abstract

This paper presents a method of pseudo-formal linearization based on the orthogonal polynomial approximation for nonlinear systems. The given nonlinear system is piecewise linearized by the formal linearization approach using the Legendre, Chebyshev, Hermite, or Laguerre polynomial functions. The resulting formal linear systems are smoothly united into a single linear one by an automatic choosing function. A nonlinear observer is synthesized as an application of this method. Numerical examples show that the accuracy of approximation by this method is greatly improved when appropriate orthogonal polynomial functions are chosen.