Robust Synchronization Preserving Model Reduction of Lur'e Networks (I)

This paper considers a model order reduction problem that reduces the complexity of interconnected Lur'e-type subsystems. The system consists of multiple identical Lur'e subsystems that evolve on a connected undirected graph. A sufficient condition of the robust synchronization of the Lur'e network is first related to the passivity of a linear time-invariant auxiliary system. Consequently, a passivity preserving model reduction scheme is applied to the auxiliary system, leading to reduced-order Lur'e subsystems, and the resulting reduced network system still robustly synchronizes. In addition, an textit{a prior} error bound between the full-order and reduced-order Lur'e subsystem is provided and the proposed method is illustrated by an example