Counterexamples to pole placement by static output feedback Original Research Article

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.