Stability analysis of discrete 2-D autonomous systems

In this paper, we analyze the ℓ
²
-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 ℓ
²
-stability and the ℓ
^∞
-stability of discrete 2-D autonomous systems, which are easy to check.