Robust stability under additive perturbations

We consider a MIMO linear time-invariant feedback system
¹
S(P, C)
which is assumed to be
u
-stable. The plant
P
is subjected to an additive perturbation
\Delta P
which is proper but not necessarily stable. We prove that the perturbed system is
u
-stable if and only if
\Delta P[I + Q.\Delta P]^{-1}
is
u
-stable. (Here
Q: = C(I + PC)^{-1}.)