Robust H∞ synchronization behavior for nonlinear stochastic coupled networks with time delays and noises

This paper studies a robust synchronization of nonlinear stochastic coupled networks under time-delays and environmental noises. A nonlinear stochastic dynamic model with time delays is proposed for describing a coupled nonlinear network under time delays, intrinsic parameter fluctuations, and extrinsic disturbances. We propose a robust synchronization criterion for attenuating these intrinsic parameter fluctuations and compensating process delays to achieve robust synchronization of nonlinear stochastic coupled networks from the nonlinear stochastic stability perspective. Furthermore, in order to avoid solving the complicated Hamilton-Jacobi inequalities (HJI) for the robust synchronization behavior, based on Takagi-Sugeno (T-S) fuzzy time-delay model and linear matrix inequalities (LMIs) technique, a systematic synchronization is proposed. Finally, a simulation example of coupled Brusselator systems is provided to illustrate our main results.