• Let G(s) have full column normal rank. Then z0Î C is a transmission zero if and only if there exists a vector 0¹u0 such
that G(z0)u0=0.
not true if G(s) does not have full column normal rank:
G has no transmission zero but G(s)u0 = 0 for
all s.
z0 can be a pole of G(s) even though G(z0) is not defined. (however G(z0) u0 may be well defined.)
For example,
Then G(1) u0 = 0. Therefore, 1 is a transmission zero.