Minimal Controllability Problem of Structural Networked Systems with MIMO Singular Subnets

This paper explores the issue of identifying the minimum input matrices needed to guarantee the structural controllability of networked dynamic systems with MIMO singular subsystems, The global graph of the system is decomposed into a network topology graph and a node graph. Regarding the network topology graph, an algorithm is proposed to identify all possible controlled nodes and to further classify the system nodes. Additionally, necessary and sufficient conditions for achieving structurally controllable network topologies that satisfy both input connection and rank conditions are provided. Based on these conditions, we determine the minimum number of controlled subnets and the input configuration subnet set to achieve structural controllability of the network topology. As for the node graph, DM decomposition is employed to derive the minimum non-dedicated input matrix, ensuring the structural R-controllability of singular subnets. Finally, by combining the network topology graph with the node graph, we can determine the minimum input matrix required for achieving global network control.