On the Connections Between Various Stability Notions for Linear 2-D Discrete Models

In this article, we review different stability definitions that have been used in the literature concerning 2-D Roesser or Fornasini–Marchesini models: structural stability, asymptotic stability, and two different notions of exponential stability. We clarify the relations between all these definitions for the linear case: the two notions of exponential stability and structural stability are all equivalent and they imply asymptotic stability.