Some results on systems described by convolutional equations

In this paper, convolutional systems in the behavioral approach are considered. Convolutional equations generalize both differential and delay-differential systems. Three fundamental problems are treated and solved. The first consists of characterizing two kernel representations when they are equivalent, i.e., to determine when two different convolutional equations provide the same set of solutions. The second problem deals with the characterization of the spectral controllability for this class of systems. The third problem provides a partial solution of the so called latent variable elimination problem, which is one of the basic steps of the modeling procedure in the behavioral approach.