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Pole Placement by Static Output Feedback for Generic Linear Systems

We consider linear systems with m inputs, p outputs, and McMillan degree n such that n=mp. If both m and p are even, we show that there is a nonempty open (in the usual topology) subset U of such systems, where the real pole placement map is not surjective. It follows that, for each system in U, there exists an open set of pole configurations, symmetric with respect to the real line, which cannot be assigned by any real static output feedback.