Abstract
In this paper, we discuss a robust synchronization problem for nonlinear stochastic coupling networks through Poisson diffusions. In the robust synchronization problem, we study the asymptotical synchronizability in probability of the nonlinear stochastic coupling networks through Poisson diffusion via a Hamilton-Jacobi inequality (HJI) criterion. Further, in order to effectively filtrate external disturbances of the nonlinear stochastic coupling networks, synchronization robustness can be guaranteed by solving a HJI. That is, by solving these two HJI criteria, not only the asymptotical synchronizability in probability, but also the robust synchronizability is guaranteed. For simplifying the HJI criteria, linear matrix inequality (LMI) criteria are proposed based on the Takagi-Sugeno (T-S) fuzzy model. Finally, we propose an algorithm for the minimal coupling design to reduce the redundant Poisson diffusion couplings of the coupling networks without losing its asymptotical synchronizability in probability and synchronization robustness. A simulation example is provided to illustrate the minimal coupling design procedure and verify the robust synchronizability.