Invariant Zeros

(state space characterizations)

(state space characterizations)

• The poles and zeros of a
transfer matrix can also be characterized in terms of its state space
realizations:

Consider the following system matrix

• Suppose has full column normal rank.
Then *z**0* is an
invariant zero iff there exist *0*¹* **x*Î **C**n and *u*Î **C**m such that

Moreover, if *u* = 0, then *z**0* is also a non-observable mode.