On the Realization of 2-D Linear Systems With Recursively Computable Latent Variable Models

In this paper, a new latent variable model is proposed for the realization of 2-D single-input-single-output linear causal systems. For the general (n, m)th-order 2-D system, the latent variable model obtained here is implicit when nnem. Importantly, however, even in this case, the model is recursively computable. The advantage of the proposed realization is that the dimension of the latent variable is nm, which is much smaller than that for existing latent variable realizations, such as Fornasini-Marchesini (FM) and Roesser models. Given a particular 2-D system, an algorithm is developed for further reducing the size of the realization.