Counterexamples to pole placement by static output feedback

@inproceedings{Eremenko2002CounterexamplesTP,
  title={Counterexamples to pole placement by static output feedback},
  author={A. Eremenko and Andrei Gabrielov},
  year={2002}
}
We consider linear systems with inner state of dimension n, with m inputs and p outputs, such that n = mp, min{m,p} = 2 and max{m,p} is even. We show that for each (m,n, p) satisfying these conditions, there is a non-empty open subset U of such systems, where the real pole placement map is not surjective. It follows that for systems in U , there exist open sets of pole configurations which cannot be assigned by any real output feedback. 

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