  As a generalization of Postnikov's construction (see arXiv: math/0609764), we
define a map from the space of edge weights of a directed network in an annulus
into a space of loops in the Grassmannian. We then show that universal Poisson
brackets introduced for the space of edge weights in arXiv: 0805.3541 induce a
family of Poisson structures on rational-valued matrix functions and on the
space of loops in the Grassmannian. In the former case, this family includes,
for a particular kind of networks, the Poisson bracket associated with the
trigonometric R-matrix.
