  We study the impedance functions of conservative L-systems with the unbounded
main operators. In addition to the generalized Donoghue class $\sM_\kappa$ of
Herglotz-Nevanlinna functions considered by the authors earlier, we introduce
"inverse" generalized Donoghue classes $\sM_\kappa^{-1}$ of functions
satisfying a different normalization condition on the generating measure, with
a criterion for the impedance function $V_\Theta(z)$ of an L-system $\Theta$ to
belong to the class $\sM_\kappa^{-1}$ presented.
  In addition, we establish a connection between "geometrical" properties of
two L-systems whose impedance functions belong to the classes $\sM_\kappa$ and
$\sM_\kappa^{-1}$, respectively. In the second part of the paper we introduce a
coupling of two L-system and show that if the impedance functions of two
L-systems belong to the generalized Donoghue classes
$\sM_{\kappa_1}$($\sM_{\kappa_1}^{-1}$) and
$\sM_{\kappa_2}$($\sM_{\kappa_2}^{-1}$), then the impedance function of the
coupling falls into the class $\sM_{\kappa_1\kappa_2}$. Consequently, we obtain
that if an L-system whose impedance function belongs to the standard Donoghue
class $\sM=\sM_0$ is coupled with any other L-system, the impedance function of
the coupling belongs to $\sM$ (the absorbtion property). Observing the result
of coupling of $n$ L-systems as $n$ goes to infinity, we put forward the
concept of a limit coupling which leads to the notion of the system attractor,
two models of which (in the position and momentum representations) are
presented. All major results are illustrated by various examples.
