vEach loop has the
open-loop transfer function as *1/s* so each loop has phase margin *f*max=-*f*min=*90**o* and gain margin *k*max=0, *k*min=*¥*

vSuppose one loop transfer
function is perturbed

Denote *z(s)/w(s)=-T**11**(s) = -1/(s+1).* Then the maximum
allowable perturbation is ||*d*||¥ <1/||*T**11**(s)*||¥ =1, which is independent of *a*.

vHowever, if both loops are
perturbed at the same time, then the maximum allowable perturbation is much smaller,
as shown below

The
system is robustly stable for every such *D** *iff

Continued.