qSuppose the controller
implemented in the system (or plant *G**22*) is actually

with a nominal value *k*=1. Then the closed-loop
system A-matrix becomes

The characteristic
polynomial has the form

With *a**1**= **a**+**b**-4+2(k-1)**ab**, a**0**=1+(1-k)**ab*

- necessary for
stability: *a**0*>0 and *a**1*>0.

-a>>1 and b>>1 and k¹1 Þ *a**0
*» *(1-k)**ab*, and *a**1 *» *2(k-1)**ab*

-a>>1 and b>>1 (q and s), the system is unstable for arbitrarily small perturbations in *k* in either direction.
Thus, by choice of *q*
and s the gain margins may be made
arbitrarily small.