Passive impedance systems with losses of scattering channels
A new model of the passive impedance system with minimal losses of scattering channels and with bilaterally stable evolution semigroup is studied. In the case of discrete time, the passive linear stationary bilaterally stable impedance system $\Sigma$ is considered as a part of some minimal scatter...
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| Date: | 2007 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2007
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/3335 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | A new model of the passive impedance system with minimal losses of scattering channels and with bilaterally stable evolution semigroup is studied.
In the case of discrete time, the passive linear stationary bilaterally stable impedance system $\Sigma$ is considered as a part of some minimal scattering-impedance
lossless transmission system, that has a $(\tilde{J}_1, \tilde{J}_2)$-unitary system operator and a bilaterally $(J_1, J_2)$-inner (in certain weak sense) transmission function in the
unit disk 22-block of which coincides with the impedance matrix of system $\Sigma$, belongs to the Caratheodory class, and has a pseudocontinuation. If the external
space of the system $\Sigma$ is infinite-dimensional, then instead of the last mentioned property, we consider more complicated necessary and sufficient conditions on the
impedance matrix of the system $\Sigma$. Different kinds of passive bilaterally stable impedance realizations with minimal losses of scattering channels
(minimal, optimal, *-optimal, minimal and optimal, minimal and *-optimal) are studied. |
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