If response is defined as $Res=\sum_{i=1}^{4} r_i x_i$ and $x=(x_1;x_2;x_3;x_4)$. $y$ is constant.
And
$\frac{d}{dt} x = P(y) \cdot x + Q(y)$
Then, how can we pick $r_i$'s such that the steady state Response is independent of $y$?
I have no idea how to even begin on this question. Note: $P$ and $Q$ are 4x4 and 4x1 matrices which have some elements as a function of $y$.
Additional note: $\sum x_i=1$ but we are told not to pick an obvious choice for r's. So I am pretty sure that the obvious choice is $r_i=1$ for all $i$.