Behaviors defined by rational functions

In this article behaviors defined by ‘differential equations’ involving matrices of rational functions are introduced. Conditions in terms of controllability, observability, and stabilizability for the existence of rational representations that are prime over various subrings of the field of rational functions are derived. Elimination of latent variables, (observable) image-like representations of controllable systems, and the structure of the rational annihilators of a behavior are discussed.