I'm studying control theory and saw this picture explaining some of the basic rules.

enter image description here

My question is if we could also say that Y(s) = (G2(s) * G1(s)) * U(s)

Or Y(s) = U(s) * G2(s) * G1(s)

I'm thinking yes.

  • 1
    $\begingroup$ No, this is not true for multiple-input multiple-output (MIMO) systems. $\endgroup$
    – RTJ
    Mar 23, 2015 at 11:41

1 Answer 1


You can do that only in SISO case. Also, I think also the picture is in the wrong order. Think of $u$ and $y$ as vectors and $G_1$ and $G_2$ as transfer function matrices. Then, the output of $G_1$ would be $G_1(s) u(s)$, which is the input for $G_2$. So $y(s) = G_2(s) G_1(s) u(s)$.


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