Transforming interconnected systems and ladder circuits into implicit 2D models

In this paper, we consider two classes of spatially interconnected systems (including ladder circuits) modelled as mixed discrete-continuous linear 2D systems. Within the algebraic analysis approach to linear systems theory, we prove that these systems can always be transformed into equivalent implicit Roesser models. Moreover we show that ladder circuits can also be transformed into equivalent implicit Fornasini-Marchesini models. An advantage of our results compared to previous ones obtained through the zero coprime system equivalence approach is that the dimension of the state vector of the equivalent Roesser (or Fornasini-Marchesini) models is significantly smaller.