Observer Design for a Class of 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 for a broader class of discrete-time nonlinear systems by using the exact linearization technique that is based on the differential geometric approach.