An Immersion-Based Observer Design for Rank-Observable Nonlinear Systems

In this note, an observer design for a wide class of nonlinear systems is proposed. It is based on some high-gain design for the particular case of state affine systems up to triangular nonlinearity on the one hand, and immersion of nonlinear systems into such a form on the other hand. Conditions for the observer convergence are given in terms of appropriate excitation, and a constructive procedure for the immersion is presented. The methodology is illustrated by examples of application