A complete stability analysis of planar discrete-time linear systems under saturation

A complete stability analysis is performed on a planar discrete-time system of the form x(k+1)=sat(Ax(k)), where A is a Schur stable matrix and sat is the saturation function. Necessary and sufficient conditions for the system to be globally asymptotically stable are given. In the process of establishing these conditions, the behaviors of the trajectories are examined in detail.