Stability and stabilizability of 2D behaviors

In the paper stability and stabilizability properties are analysed in the context of two-dimensional (2D) behaviors, Searching for a comparison with traditional 2D input/output and state-space models, the interest is focused on linear, shift-invariant, complete behaviors whose autonomous part updates according to a quarter-plane causality law. For this class of behaviors, stability and stabilizability definitions are introduced and related to the varieties of certain ideals, which can be obtained by suitably factorizing the Laurent polynomial matrices involved in the behavior description