Pinning synchronization control for stochastic multi-layer networks with coupling disturbance. (September 2022) - Sun, Shixiang; Ren, Tao; Xu, Yanjie
Abstract: The pinning synchronization scheme is investigated for stochastic multi-layer networks under the intra-layer coupling disturbance and stochastic noise. To save the control cost, a pinning control scheme is proposed. And some sufficient conditions in the form of the LMI are given, based on Lyapunov theory and stochastic analysis, to make sure that the multi-layer networks synchronize to a desired trajectory. Next, the selection scheme of pinned nodes is designed according to the structure of considered multi-layer networks. Finally, simulation examples are shown to illustrate the feasibility and availability of the designed pinning scheme. Highlights: The pinning synchronization problem for the stochastic multi-layer networks with intra-layer coupling disturbance is firstly considered. A novel pinning scheme is proposed to synchronize the considered multi-layer networks. The algorithm for the selection of the pinning nodes involving the out-degree and in-degree of the nodes is designed according to the dynamical characteristic of the considered multi-layer networks.