A nonlinear synchronization scheme for polynomial systems

Synchronization phenomena among multiple subsystems have been studied in various publications using many kinds of models for a long time. This is because many subsystems are required to behave synchronously or cooperatively in many areas. For example, networks of (electro-)mechanical systems, coupled neurons, and cooperating robots. This paper presents a feedback scheme for synchronization among multiple subsystems in polynomial form using a dissipation inequality and sum of squares tools. First, we show that the problem is the same as finding an asymptotically stabilizing control for polynomial systems. Then, it is discussed how to use the stabilizing control for synchronization. The proposed scheme can be applied to several kinds of models which are in polynomial form and commonly used for synchronization research in the literature, and overcomes several drawbacks in the previous results.