A Pseudo-Formal Linearization of Polynomial Type for Nonlinear Systems and Its Applications

In this paper we consider a pseudo-formal linearization that transforms a given nonlinear system into a pseudolinear system. The given nonlinear system is linearized piecewise by the formal linearization method based on a Taylor expansion considering up to higher-order terms, and then each piecewise linearized system is smoothly united into a single linearized system by an automatic choosing function. The error bounds of this pseudo-formal linearization indicate that the accuracy of the approximation is improved when the domain is reasonably divided and as the order of the polynomials increases. A nonlinear observer and a nonlinear filter are also synthesized as applications of the pseudo-formal linearization. The high validity of this method is verified through numerical examples.