An algorithm for SDV representation of 2D behaviors

This paper deals with the characterization of 2D behaviors that are representable by means of special first order models, known as state/driving-variable (SDV) models. In previous work, [1], [2] we have shown how to identify SDV-representable behaviors using one of its full row rank representations. Here, we give a further refinement by showing that a 2D behavior is SDV-representable if and only if each of its kernel representations can be decomposed as a product of three 2D L-polynomial matrices: a zero right prime matrix, a cw-unital square matrix and a factor left prime matrix. Using that decomposition, we present a procedure to obtain SDV representations of a 2D behavior starting from any of its kernel representations.