  The article addresses the problem of strong structural controllability of
structured networks with multi-input multi-output (MIMO) node systems. The
authors first present necessary and sufficient conditions for strong structural
controllability, which involve both algebraic and graph-theoretic aspects.
These conditions are computationally expensive, especially for large-scale
networks with high-dimensional state spaces. To overcome this computational
complexity, we propose a necessary algebraic condition from a node system's
perspective and a graph-theoretic condition from a network topology's
perspective. The latter condition is derived from the structured
interconnection laws and employs a new color change rule, namely weakly color
change rule introduced in this paper. Overall, this article contributes to the
study of strong structural controllability in structured networks with MIMO
node systems, providing both theoretical and practical insights for their
analysis and design.

Systems and Control;Systems and Control