Parameterized linear systems in thebehavioral approach

In the behavioral approach a dynamical system is essentially determined by a set of trajectories B, which is called behavior. There exist various ways for representing behaviors that are linear and shift-invariant: kernel representations, image representations and latent variable representations. In this paper we deal with families of parametrized linear shift-invariant behaviors and with the problem of representing such families in an eecient way. The representation of parametrized families of behaviors we propose is based on the algebraic properties of a class of rings that are called Jacobson rings. Also in this case parametrized kernel representations, parametrized image representations, and parametrized latent variable representations play an essential role. Finally, algorithms for passing from one representation to another are proposed. This also solves the parametrized latent variable elimination problem.