Single Impulsive Controller for Exponential Synchronization of Stochastic Lur'e Networks with Impulsive Disturbance

The investigations are made on the exponential synchronization of the stochastic Lur'e system with nonlinear coupling and impulsive disturbance. The impulsive effects in complex networks could play a positive or a negative role for synchronization. For the sake of simplification and efficiency, a single impulsive controller is designed to realize the synchronization of the impulsive dynamical network with respect to stabilizing and destabilizing impulsive effects. Sufficient conditions are derived to guarantee the realization of the exponential synchronization for all initial values by means of the Lyapunov stability theorem, the comparison principle, and the linear matrix inequalities (LMIs). Numerical simulations are given to support the validity of the analytical results.