## 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.

Original language | English |
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Pages (from-to) | 529-559 |

Number of pages | 31 |

Journal | Linear Algebra and Its Applications |

Volume | 610 |

DOIs | |

State | Published - 1 Feb 2021 |

## Keywords

- Operator vessel
- Overdetermined 2D system
- Pole placement

## ASJC Scopus subject areas

- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics