  We formulate and solve a pole placement problem by state feedback for
overdetermined 2D systems modeled by commutative operator vessels. In this
setting, the transfer function of the system is given by a meromorphic bundle
map between two holomorphic vector bundles of finite rank over the
normalization of a projective plane algebraic curve. The obstruction for a
solution is given by an existence of a certain meromorphic bundle map on the
input bundle. Reducing to the 1D case, this gives a functional obstruction
which is equivalent to the classical pole placement theorem. Our result
improves on, and gives a new approach to pole placement even in the classical
case, and answers a question of Ball and Vinnikov.
