On a pseudo-formal linearization using automatic choosing function for multidimensional systems and its application to nonlinear observer

In this paper we consider an evolutional approach of a formal linearization method based on Taylor expansion exploiting an automatic choosing function for multidimensional nonlinear systems. Nonlinear systems are linearized piecewise by the formal linearization method using Taylor expansion considering up to the higher order terms, and these linearized systems can be united into one linear system with respect to a linearization function by applying an automatic choosing function. An algorithm of this new linearization approach for multidimensional nonlinear systems is presented and its application to a nonlinear observer is proposed.