Observer design for discrete-time nonlinear systems

Necessary and sufficient conditions are presented under which a discrete-time autonomous system with outputs is locally diffeomorphic to an output-scaled linear observable system or an output-scaled nonlinear system in the observer form. As a consequence of such characterizations, the nonlinear observer design problem is studied by a time-scaling approach combined with the exact linearization technique, for a broader class of discrete-time nonlinear systems.