UPDATE: SOLVED! Turns out the problem was simply a matter of taking two Laplace transforms and generating four different differential equations in terms of Y1/U1, Y1/U2, Y2/U1, and Y2/U2.

I have a few questions about part A of this problem:

I think I understand the general idea of what a deviation variable is supposed to do, it just sounds like a measured response to the deviation from the models steady state. Here it sounds like a few transfer functions can be make out of the two equations listed in the problem, but I'm not exactly sure how to do it. So far in the class I'm taking we have only used simplified transfer functions and used Laplace transforms to solve for Y(s)/U(s) once in the Laplace domain.

I have done some digging on the internet and found what I think might be a useful example, but I still don't know where to begin in putting the first two equations into deviation variable form.

I posted the example here:

Would the problem require 4 different equations in deviation variable form since there are both two inputs and two outputs?

Any help at all here would be greatly appreciated, I'm really stuck on the whole concept of this question. I was never very good at differential equations.