Approximate high-gain observers for uniformly observable nonlinear systems

A methodolgy for the design of continuous practical observers for nonlinear uniformly observable systems is presented. The system is first transformed into observability normal form, using the observability map semi-diffeomorphism. Since this normal form may have a non-Lipschitz continuous right hand side, a so called ε-approximate high-gain observer is designed for it, constituting the dynamic part of the observer. The inverse of the transformation is used as the static part. Convergence of the observer´s state trajectory to a ball around the true state trajectory is guaranteed, with the radius of the, ball as small as desired