On blocking zeros in linear multivariable systems

In this note, the concept of a "blocking zero" is introduced and the relationship between blocking zeros and other zeros (transmission, invariant, system) is discussed. It is shown that the existence of an uncontrollable and/or unobservable mode in a given state-space description of a multiinput, multioutput system is equivalent to a pole-blocking zero cancellation. This can be regarded as an extension of some results which are well known for single-input and/or single-output systems but cannot be extended to multiinput, multioutput systems using the existing types of zeros.