Synchronization of Lur’e Networks via Heterogeneous Unknown Interconnections

This brief deals with synchronization of Lur’e networks diffusively coupled through heterogeneous unknown relative-state interconnections over connected undirected graphs. While the node nonlinearities are identical, unknown and incrementally sector-bounded, the edge nonlinearities are different, unknown and sector-bounded. These Lur’e nonlinearities can be regarded as model uncertainties or interconnection constraints. The S-Lemma and LMI techniques are employed following the absolute stability theory of Lur’e systems. In contrast to the case of homogeneous linear relative-state interconnections, here the obtained synchronization criterion is given by two isotypic LMIs, which involve the smallest and respectively the largest nonzero Laplacian eigenvalues. Finally, numerical simulations are presented to illustrate the effectiveness of the theoretical results.