Finding transfer function by linear system
assuming those &quot;*&quot; symbols are convolution, just algebra, no?
$$
\begin{align}
Z(s) &amp;= H_1(s)X(s) \\
W(s) &amp;= Z(s)+H_3(s)Y(s) =&gt; W(s)  = H_1(s)X(s)+H_3(s)Y(s) \\
Y(s) &amp;= H_2(s)W(s) =&gt; \frac{Y(s)}{H_2(s)}
\end{align}
$$
$$
\begin{align}
\frac{Y(s)}{H_2(s)} = H_1(s)X(s)+H_3(s)Y(s)  \\
Y(\frac{1}{H(s)}-H_3(s)) = H_1(s)X(s) \\
\frac{Y(s)}{X(s)} =&gt; \frac{H_1(s)}{\frac{1}{H_2(s)}-H_3(s)}
\end{align}
$$