Strong Structural Controllability of Structured Networks with MIMO node systems

Abstract: 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.