Resumen de Characterizing controllable subspace and herdability of signed weighted networks via graph partition
Herdability is a variant of controllability, and is an indicator of the ability to drive system states to a specific subset of the state space. This paper characterizes the controllable subspace and herdability of signed weighted networks. Specifically, a dynamic signed leader–follower network is considered, in which a small subset of the network nodes (i.e., the leaders) is endowed with exogenous control input and the remaining nodes are influenced by the leaders via the underlying network connectivity. The considered network permits positive and negative edges to capture cooperative and competitive interactions, resulting in a signed graph. Motivated by practical application, the system states are required to be driven by the leaders to be element-wise above a positive threshold, i.e., a specific subset rather than the entire state space as in classical controllability. Graph partitions are exploited to characterize the controllable subspace of the system, from which sufficient conditions are derived to render the system herdable. It is revealed that the quotient graph can be used to infer the herdability of the original graph, wherein criteria of the herdability of quotient graphs are developed based on positive systems. Examples are provided to illustrate the developed topological characterizations.
