Construct the signal flow graph for the following set of simultaneous equations: X₂ = A21 X₁ + A23 X3, X3 = A31 X1 + A32 X2 + A33 X3, X4 = A42X2 + A43X3. Identify the (a) input node, (b) output node, (c) forward paths, (d) feedback paths, and (e) self-loop.

Given:

Input output equations of a control system,

$$\begin{gathered} x_2=A_{21}{x}_1+A_{23}{x}_3 \\ {x}_3=A_{31}{x}_1+A_{32}{x}_2+A_{33}{x}_3 \\ {x}_4=A_{42}{x}_2+A_{43}{x}_3 \end{gathered}$$

To find:

we have construct signal flow graph from given equations.

And identify the

a) input node

b) output node

c) forward paths

d) feedback paths

e) self loop