Model Reduction of Synchronized Lur'e Networks

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