Strong structural controllability of structured networks with MIMO node systems

This paper addresses the problem of strong structural controllability of structured networks with multi-input multi-output (MIMO) node systems. A necessary and sufficient condition is firstly presented for strong structural controllability. The condition is somewhat restrictive and computationally expensive, especially for large-scale networks with high-dimensional state spaces. To overcome this computational complexity, several necessary algebraic conditions are established from the perspectives of both the node dynamics and the structured interconnection laws, respectively. Furthermore, by utilising the so-called weakly colour change rule, a graph-theoretic method is provided to assess the condition from the perspective of the structured interconnection laws.