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Passive impedance systems with losses of scattering channels

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Abstract

We consider a new model of passive impedance system with minimum losses of scattering channels and bilaterally stable evolutionary semigroup. In the case of discrete time, the passive linear stationary bilaterally stable impedance system Σ is regarded as a part of a certain minimal lossless transmission system with a \((\tilde J_1 ,\tilde J_2 )\)-unitary system operator and a bilaterally (J 1, J 2)-inner (in a certain weak sense) transfer function in the unit disk whose 22-block coincides with the impedance matrix of the system Σ, belongs to the Carathéodory class, and possesses a pseudoextension. If the external space of the system Σ is infinite-dimensional, then, instead of the last property, we consider more complicated necessary and sufficient conditions for the impedance matrix of the system Σ. We study passive bilaterally stable impedance realizations with minimum losses of scattering channels (minimum, optimal, *-optimal, minimum and optimal, and minimum and *-optimal).

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 5, pp. 618–649, May, 2007.

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Arov, D.Z., Rozhenko, N.A. Passive impedance systems with losses of scattering channels. Ukr Math J 59, 678–707 (2007). https://doi.org/10.1007/s11253-007-0045-9

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  • DOI: https://doi.org/10.1007/s11253-007-0045-9

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