Synchronization of linear agents with sector-bounded input nonlinearities

This paper is concerned with the local synchronization of linear agents subject to sector-bounded input nonlinearities over an undirected communication graph. We first derive a sufficient LMI condition for achieving the local synchronization for any nonlinearities satisfying a given sector condition. Based on this analysis, we present a sufficient LMI synthesis condition of a relative state feedback protocol which locally synchronizes the linear agents with arbitrary sector-bounded input nonlinearities. The desired protocol can be efficiently obtained via convex optimization, since the present synthesis condition is convex in the decision variables and is independent of the size of the communication graph.