Consider the feedback composition with two LTI systems:
The circle adds z to x. The signals are related by
y = S1(u) = S1(x + z ) = S1(x) + S1(z)
since S1 is linear. Since z = S2(y),
y = S1(x) + S1(S2(y))
It is possible to use this to show that this system is LTI (see the text).