Some properties of minimum phase systems and "Squared-down" systems

It is shown that a minimum phase system implies certain properties of the system itself. In particular, a system which has equal inputs and outputs, and which is minimum phase automatically, implies that the system must be stabilizable and detectable. It is also shown that "squaring down" a system which has more inputs than outputs, to produce a system which has equal inputs and outputs, may be an undesirable procedure to carry out, in the sense that the original nonsquared system may be minimum phase, but the "squared-down" system may in fact now be nonminimum phase.