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On unimodular transformations of conservative L-systems | | Sergey Belyi
; Konstantin Makarov
; Eduard Tsekanovskii
; | | Date: |
30 Aug 2016 | | Abstract: | We study unimodular transformations of conservative $L$-systems. Classes
$sM^Q$, $sM^Q_kappa$, $sM^{-1,Q}_kappa$ that are impedance functions of
the corresponding $L$-systems are introduced. A unique unimodular
transformation of a given $L$-system with impedance function from the mentioned
above classes is found such that the impedance function of a new $L$-system
belongs to $sM^{(-Q)}$, $sM^{(-Q)}_kappa$, $sM^{-1,(-Q)}_kappa$,
respectively. As a result we get that considered classes (that are
perturbations of the Donoghue classes of Herglotz-Nevanlinna functions with an
arbitrary real constant $Q$) are invariant under the corresponding unimodular
transformations of $L$-systems. We define a coupling of an $L$-system and a so
called $F$-system and on its basis obtain a multiplication theorem for their
transfer functions. In particular, it is shown that any unimodular
transformation of a given $L$-system is equivalent to a coupling of this system
and the corresponding controller, an $F$-system with a constant unimodular
transfer function. In addition, we derive an explicit form of a controller
responsible for a corresponding unimodular transformation of an $L$-system.
Examples that illustrate the developed approach are presented. | | Source: | arXiv, 1608.8583 | | Services: | Forum | Review | PDF | Favorites | |
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