DISO System

A DISO system is one with two inputs and one output.

It has the input/output relation:

$$Y(s)=\left[\begin{array}{cc}{G}_1(s)& G_2(s)\end{array}\right]\left[\begin{array}{c}{U}_1(s)\\ U_2(s)\end{array}\right]=G_1(s)U_1(s)+G_2(s)U_2(s)$$

Misleading View

Note that the two blocks below are algebraically equivalent, but it’s better to view them as a single inseparable system.

$$\begin{array}{rl}G(s)& =\frac{\mathbf{b}(s)}{a(s)}=\frac{1}{a(s)}\left[\begin{array}{cc}{b}_1(s)& b_2(s)\end{array}\right]\\ & =\frac{\left[\begin{array}{cc}{b}_{10}{s}^n+\cdots +b_{1n}& b_{20}{s}^n+\cdots +b_{2n}\end{array}\right]}{a_0{s}^n+a_1{s}^{n-1}+\cdots +a_n},a\ne 0\end{array}$$