Model Reduction of Synchronized Lur'e Networks
Xiaodong Cheng, Jacquelien M. A. Scherpen · University of Groningen research database (University of Groningen / Centre for Information Technology) · 2019
In this talk, we investigate a model order reduction scheme that reduces the complexity of uncertain dynamical networks consisting of diffusively interconnected nonlinear Lure subsystems. We aim to reduce the dimension of each subsystem and meanwhile preserve the synchronization property of the overall network. Using the upper bound of the Laplacian spectral radius, we first characterize the robust synchronization of the Lure network by a linear matrix equation (LMI), whose solutions can be treated as generalized Gramians of each subsystem, and thus the balanced truncation can be performed on the linear component of each Lure subsystem. As a result, the dimension of the each subsystem is reduced, and the dynamics of the network is simplified. It is verified that, with the same communication topology, the resulting reduced network system is still robustly synchronized, and the a priori bound on the approximation error is guaranteed to compare the behaviors of the full-order and reduced-order Lure subsystem