Abstract
A linear behavior is defined essentially as a family of finite but sufficiently long trajectories that is invariant with respect to restriction operators. This may be singular in the sense that it may contain trajectories that 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−1R is proper. A canonical one-to-one correspondence is established between linear behaviors and equivalence classes of AR-models. The result is a natural generalization of a well-known result due to Willems.
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