Clustered Model Reduction of Large-Scale Bidirectional Networks

This chapter proposes a clustered model reduction method for interconnected linear systems evolving over bidirectional networks. This model reduction method belongs to a kind of structured model reduction methods, where network clustering, namely clustering of subsystems, is performed according to a notion of uncontrollability of local states. We refer to this notion of uncontrollability as cluster reducibility, which can be captured by a coordinate transformation called positive tridiagonal transformation in an algebraic manner. In this chapter, it is shown that the aggregation of the reducible clusters retains the stability of the original system as well as an interconnection topology among clustered subsystems. Furthermore, an \(\fancyscript{H}_{\infty }\)-error bound is derived for the state discrepancy due to the cluster aggregation. The efficiency of the clustered model reduction is shown through an example of large-scale complex networks.