Stability analysis of discrete 2-D autonomous systems

In this paper, we analyze the ℓ²-stability and the ℓ^∞-stability of general discrete 2-D autonomous systems. The problem of ℓ^∞-stability has not been studied before for general 2-D autonomous systems. We give a necessary condition for the ℓ^∞-stability of discrete 2-D autonomous systems. We also give sufficient conditions for the ℓ²-stability and the ℓ^∞-stability of discrete 2-D autonomous systems, which are easy to check.