  This work is a direct continuation of the authors work arXiv:0812.3779v1. A
special case of conservative overdetermined time invariant 2D systems is
developed and studied. Defining transfer function of such a systems we obtain a
class CI of inner functions $S(\lambda,t_2)$, which are identity for
$\lambda=\infty$, satisfy certain regularity assumptions and intertwines
solutions of ODEs with a spectral parameter $\lambda$. Using translation model,
we prove that every function in the class CI can be realized as a transfer
function of a certain vessel.
  The highlight of this theory is a generalization Potapov's theorem, which
gives a very special formula for such a function in the form of multiplication
of Blacke-Potapov products, corresponding to the discrete spectrum of certain
system operator $A_1(t_2)$ and of multiplicative integral, corresponding to the
continuous spectrum of $A_1(t_2)$. This theorem is proved under a slightly more
restrictive assumptions, then the development of the whole theory. Namely, we
suppose that the derivative of the transfer function is a continuous function
of $t_2$ for almost all $\lambda$.
  At the last part zero/pole interpolation problem for matrix functions in CI
is considered and a realization theorem of such functions appeared in
arXiv:0812.3779v1 (theorem 8.1) is reproved. Hermitian case is also analyzed
and the corresponding realization theorem is proved.
