Global pinning synchronization of stochastic delayed complex networks

Abstract

In this paper, the global pinning synchronization problem of a class of complex dynamical networks with hybrid couplings, time delays, random data packet dropouts and multiple stochastic disturbances is investigated. The hybrid couplings are portrayed in three forms: constant couplings, discrete-delay couplings and distributed-delay couplings. The phenomenon of random packet dropouts is described as a binary random variable which obeys the Bernoulli distribution taking values of 0 and 1 with a certain probability. Multiple noisy processes herein are characterized by Brownian motions, which act on all coupling terms as well as the overall dynamics equation. By applying the Lyapunov method and stochastic analysis technique, sufficient conditions are established to ensure the considered stochastic delayed complex network to globally synchronize to a reference trajectory in the mean-square sense via the developed randomly occurring pinning control strategy. The obtained criteria are within the framework of linear matrix inequations. Finally, a simulation example is presented to verify the feasibility and effectiveness of the derived theoretical results.