Clustered model reduction of networked dissipative systems

In this paper, we propose a clustered model reduction method for networked dissipative systems, which consist of identical subsystems having a dissipative property. In the clustered model reduction, we perform both network structure simplification and subsystem approximation, implemented as block-diagonally structured orthogonal projection. To develop this model reduction method, we derive a condition for the existence of block-diagonal Lyapunov functions for networked dissipative systems, given as a matrix inequality that involves interconnection matrices and supply functions. It turns out that the existence of such a structured Lyapunov function is key to guaranteeing stability preservation. In addition, we perform an approximation error analysis in terms of the ℋ2-norm. The efficiency of the proposed method is demonstrated though numerical experiments for interconnected passive systems.