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arXiv · 1712.07550

Pole placement for overdetermined 2D systems

Liran Shaul·Victor Vinnikov
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Abstract

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.

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Liran Shaul, Victor Vinnikov. 2017-12-20. Pole placement for overdetermined 2D systems. https://doi.org/10.1016/j.laa.2020.10.008

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