  This paper studies the problem of designing networks that are strong
structurally controllable, and robust simultaneously. For given network
specifications, including the number of nodes $N$, the number of leaders $N_L$,
and diameter $D$, where $2 \le D \le N/N_L$, we propose graph constructions
generating strong structurally controllable networks. We also compute the
number of edges in graphs, which are maximal for improved robustness measured
by the algebraic connectivity and Kirchhoff index. For the controllability
analysis, we utilize the notion of zero forcing sets in graphs. Additionally,
we present graph grammars, which are sets of rules that agents apply in a
distributed manner to construct the graphs mentioned above. We also numerically
evaluate our methods. This work exploits the trade-off between network
controllability and robustness and generates networks satisfying multiple
design criteria.
