We provide some new necessary and sufficient conditions which guarantee arbitrary pole placement of a particular linear system over the complex numbers. We also exhibit a non-trivial real linear system which is not controllable by real static output feedback and discuss a conjecture from algebraic geometry concerning the existence of real linear systems for which all static feedback laws are real.
For an amplification of our example of a non-trivial real linear system
which is not controllable with real output feedback, a further
discussion of computational issues, and the MAPLE/SINGULAR scripts we
used, click here.