A new look on poles and zeros at infinity in the light of systems interconnection

Due to the recent developments of the "behavioral approach" and of the "module-theoretic approach" of linear systems, there is a need to clarify and unify the theory of "impulsive motions". This is done here using (i) the theory of distributions, (ii) the notion of "temporal interconnection" (interconnection from an initial time or up to a final time) and (iii) some algebraic developments based on the module theory and its relationship with the behavioral representations. The general case of time-varying systems is treated. Several examples illustrate the theory.