Nonlinear Observer Based on Cascade Form and Output Injection

Abstract

This paper deals with the transformation of a nonlinear system into a cascade system for which an observer can be designed. This class of cascade systems contains the class of state affine systems up to output injection. The necessary and sufficient conditions required for existence of this transformation are presented first; these are extensions of some existing results. A constructive algorithm is then presented for the calculation of an adequate diffeomorphism which transforms the original system to the desired cascade form. The characterization of a set of all such diffeomorphisms is presented in the end.