q Recall
(bopt(P)) 2 £|N0(s)Nz(s)|2 +|M0(s)Np(s)|2 " Re(s)>0
q Let s=rejq and note that Nz(zi)=0 and Np(pj)=0. Then the bound can be small if
q|Nz(s)| and |Np(s)| are both small for some
s. That is, |Nz(s)|»0 (i.e., s is close to a right-half plane zero of
P) and |Np(s)|»0 (i.e., s is close to a right-half
plane pole of P).
q This is possible if P(s) has a right-half plane zero near a right-half
plane pole. (See Example 16.1.)
q|Nz(s)| and |M0(s)| are both small for some s. That is, |Nz(s)|»0 (i.e., s is close to a right-half plane zero
of P) and |M0(s)|»0 (i.e., |P(jw)| is large around w=|s|=r ).
q This is possible if |P(jw)| is large around w=r where r is the modulus of a right-half plane zero of P (See Example16.2)