Limitations on the stabilizability of globally-minimum-phase systems

The author gives examples showing that, in general, it is possible for a globally-minimum-phase system in normal form to have states that cannot be driven asymptotically to the origin by means of any open-loop control. In particular, this provides counterexamples to a number of recently published stabilization theorems. It is established, by means of examples, that a minimum-phase system in normal form need not be semiglobally stabilizable or small-input semiglobally BIBO stabilizable, even if the zero dynamics is exponentially stable and the completeness condition holds