• Suppose
has full row normal rank. Then z0 is an invariant zero iff there exist 0¹ yÎ Cn and vÎ Cp such that
•
Moreover, if v = 0, then z0 is also a non-observable mode.
• G(s) has
full column(row) normal rank if and only if has full column (row) normal
rank.
This follows by noting that
and
• Let be a minimal
realization. Then z0 is a transmission of G(s) iff it is an invariant
zero of the minimal realization.