Passive synchronization of network of oscillators with delays: Application to antenna arrays

In this paper, time delays effects on network synchronization are tackled in the case of a network of a diffusely coupled identical systems. It is assumed that the parameters of the networks are in a polytope. Using Lyapunov methods and LMI (Linear matrix inequality) framework coupled to dissipativity theory, a new condition is given to assure global exponential synchronization. The approach is successfully applied to network of oscillators used in smart antenna application.