Pole placement for overdetermined 2D systems

Liran Shaul, Victor Vinnikov

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)529-559
Number of pages31
JournalLinear Algebra and Its Applications
Volume610
DOIs
StatePublished - 1 Feb 2021

Keywords

  • Operator vessel
  • Overdetermined 2D system
  • Pole placement

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