Making a stable discrete-time system chaotic via small-amplitude output feedback

A general approach is developed for making a given stable discrete-time system chaotic via small-amplitude scalar-valued output feedback. Provided that the given nominal discrete-time system has an exponentially stable fixed point and has a well-defined relative degree at this fixed point with respect to a system parameter, a small-amplitude scalar-valued output-feedback can make the system chaotic within a neighborhood of the fixed point.