• In other words, if stability breaks down
first then the infimum over stabilizing controllers equals the infimum over all controllers, stabilizing or
otherwise.

• In view of this, we would expect that
typically complementary
would fail first.

• Complementary failing at g=g1 means r(*X**¥*) ®¥ as
g®g1 so condition (iii) would fail at even
larger values of g , unless the eigenvectors associated with r(*X**¥*) as g®g1 are in the null space of *Y**¥*

• Thus condition (iii) is the most likely of
all to fail first.