Robust synchronization of directed Lur´e networks with incremental nonlinearities

In this paper we deal with robust synchronization problems for directed Lur´e networks subject to incrementally passive nonlinearities and incrementally sector bounded non-linearities, respectively. By making use of general algebraic connectivities of strongly connected graphs and subgraphs, sufficient synchronization conditions are obtained for diffusively interconnected identical Lur´e systems on both the strongly connected interconnection topology and the topology containing a directed spanning tree. The static feedback gain matrices are determined by the matrices defining the individual agent dynamics and the general algebraic connectivities. The synchronization criteria obtained in the present paper extend those for undirected Lur´e networks in our previous work.