• The poles and zeros of a
transfer matrix can also be characterized in terms of its state space
realizations:
Consider the following system matrix
z0 is an invariant zero of the realization if
it satisfies
• Suppose has full column normal rank.
Then z0 is an
invariant zero iff there exist 0¹ xÎ Cn and uÎ Cm such that
•
Moreover, if u = 0, then z0 is also a non-observable mode.