Robust synchronization of Lur´e networks with incremental nonlinearities

This paper deals with robust synchronization problems for networks of diffusively interconnected identical Lur´e systems subject to incrementally passive nonlinearities and incrementally sector bounded nonlinearities, respectively. Whereas in stabilization of one single Lur´e system the conditions of passivity and sector boundedness for the nonlinear feedback loop are commonly assumed, in our context of networked Lur´e systems we adopt the stronger assumptions of incremental passivity and incremental sector boundedness. Throughout this paper the interconnection topologies among these Lur´e systems are assumed to be undirected and connected. The conventional a priori assumption on the existence of a synchronization manifold is not employed in this paper. Both for the case of incrementally passive as well as incrementally sector bounded nonlinearities we obtain necessary and sufficient conditions for the existence of the sufficient distributed robustly synchronizing protocols. The static feedback gains are computed by solving LMI´s in terms of the matrices defining the individual agent dynamics.