Equivalence between different stability definitions for 2D linear discrete Roesser models

In this paper, we review different stability definitions that have been used in the literature concerning 2D Roesser models: structural stability, asymptotic stability, and exponential stability. We clarify the relations between all these definitions: when the considered Roesser model is linear, structural stability and exponential stability are equivalent and both of them imply asymptotic stability. However asymptotic stability does not imply exponential or structural stability. The proof is based on previous results obtained for Fornasini-Marchesini models and requires careful switching between both models.