A necessary and sufficient condition for a discrete dynamical system to be globally stable and plus-globally stable are first
established in Section 2. The V-condition is introduced and Theorems 3.5 and 3.7 are presented in Section 3. The two theorems
link the V-condition to the most relevant properties of globally stable and plus-globally stable discrete dynamical systems. In Section 4
we provide a simple application to a convergence problem for forward
neural networks.
