Singular linear behaviors and their AR-representations

A linear behavior is defined essentially as a family of finite but sufficie ntly long trajectories that is invariant with respect to restriction operat ors. This may be singular in the sense that it may contain trajectories tha t cannot be continued to the right. An AR-model is defined essentially as a pair (D, R), where D is a nonsingular rational matrix and R is a full row rank polynomial matrix such that D-1 R is proper. A canonical one-to-one co rrespondence is established between linear behaviors and equivalence classe s of AR-models. The result is a natural generalization of a well-known resu lt due to Willems.