Adaptive synchronization control for stochastic complex networks with derivative coupling

In this paper, the problem of the adaptive synchronization control is studied for a class of stochastic complex networks with unknown nonlinear coupling strength and derivative coupling. First, in order to deal with the unknown nonlinear coupling strength, Takagi–Sugeno (T–S) fuzzy method is used to transform the network model into a T–S fuzzy complex network model. Then,a fuzzy adaptive controller and the corresponding adaptive parameter update rate are designed. Subsequently, a new Lyapunov function is constructed, which is related to the derivative coupling. By employing the stochastic analysis technique and Lyapunov stability theory, a sufficient condition is given for exponential stabilization in mean square of the synchronization error system. Finally, the effectiveness of the obtained theoretical results is verified through a simulation.