Realizations of behavior for generalized chain-scattering representations

This paper introduces a notion of realization of behavior which is shown to be a generalization of the classical concept of a realization of transfer function. By using this approach, the input-output structures of the generalized chain-scattering representations (GCSRs) and the dual generalized chain-scattering representations (DGCSRs) are investigated in a behavioral theory context. Subsequently the corresponding autoregressivemoving- average (ARMA) representations are proposed and are proved to be realizations of behavior for any GCSR. Realization of behavior is particularly suitable for situations in which the coefficients are symbolic rather than numerical due to the fact that no numerical computation is involved in this approach.