Properties of generalized chain-scattering representations

Through its cascade and symmetry properties, not only can the chain-scattering representation illuminate the fundamental structure of H_∞ control systems, but also it has many applications in circuit theory and signal processing. In this paper, the classical results about cascade interconnections are generalized from the regular case to the general case of the generalized chain-scattering representations (GCSR). A notion of realization of behavior is introduced 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 (GCSR) and the dual generalized chain-scattering representations (DGCSR) are investigated in a behavioral theory context. Subsequently the corresponding autoregressive-moving-average (ARMA) representations are proposed and are proved to be realizations of behavior for any GCSR and for any DGCSR