Given a structured distributed system $S$ as in (3) composed of subsystems $S_i,~i~=~1,\ldots,r$ with graphical form denoted as $G_i(V_i,E_i,E^\ast_i)$;

for $i$ from $1$ to $r$

To subsystem $S_i$, analyze its local structural controllability using the minimum input theorem;

Obtain its maximum matching set $E_i~\ast$, the set of matched vertices $V_i~\ast$, the set of unmatched vertices $\bar{V}_i~\ast$, and the corresponding set of control inputs $U_i$;

end for

for $i$ from $1$ to $r$

Determine the expansion set $D_i$ of $S_i$ according to $E^\ast_i$ containing the interconnection information with its neighbor subsystems;

for each $x_k~x_l~\in~D_i$

If $x_l$ is a vertex with a control input in $S_j$, the control input on $x_l$ is redundant to be removed as a virtual control input;

end for

end for

Given a structured distributed system $S$ as in (3) composed of subsystems $S_i~(i~=~1,\ldots,r)$ with graphical form denoted as $G_i(V_i,E_i,E^\ast_i)$;

To subsystem $S_1$, analyze its local structural controllability using the minimum input theorem;

for $i$ from $2$ to $r$

To subsystem $S_i$, analyze its local structural controllability using the minimum input theorem;

Obtain its maximum matching set $E_i~\ast$, the set of matched vertices $V_i~\ast$, the set of unmatched vertices $\bar{V}_i~\ast$ and the corresponding set of control inputs $U_i$;

Determine its expansion set $D_i$ based on its neighbor subsystems in subsystems $S_j,~j~=~1,\ldots,i-1$, then find out and remove virtual control inputs in its neighbor subsystems;

for each $S_j(j~\in~\{1,\ldots,i-1\}$ neighbor to $S_i$

Update the expansion sets of $S_j$, then find out and remove virtual control inputs in $S_i$;

end for

end for