Model reduction of multi-input dynamical networks based on clusterwise controllability

This paper proposes a model reduction method for a multi-input linear system evolving on large-scale complex networks, called dynamical networks. In this method, we construct a set of clusters (i.e., disjoint subsets of state variables) based on a notion of clusterwise controllability that characterizes a kind of local controllability of the state-space. The clusterwise controllability is determined through a basis transformation with respect to each input. Aggregating the constructed clusters, we obtain a reduced model that preserves interconnection topology of the clusters as well as some particular properties, such as stability, steady-state characteristic and system positivity. In addition, we derive an H
_∞
-error bound of the state discrepancy caused by the aggregation. The efficiency of the proposed method is shown by a numerical example including a large-scale complex network.