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Finite-time Combinational Inner and Outer Synchronization of Multi-networks Based on Sliding Mode Control

Most existing network synchronization researches deal with two or fixed number of networks, which usually have limitations in practical application. Thus, improving the general applicability of the method becomes an issue worthy of further study in network synchronization. In this paper, on the basis of the nonsingular terminal sliding mode control (NTSMC) principle, a novel method of finite-time combinational inner and outer synchronization of multi-networks is investigated. First, a suitable network sliding surface is designed and its convergence of finite time is proved by using the Lyapunov stability theory. Then, based on the adaptive technique, some sufficient conditions are obtained, which not only can guarantee the realization of finite-time combinational inner synchronization (FTCIS) within a complex network with unknown parameters and uncertain disturbances, but also can realize the finite-time combinational outer synchronization (FTCOS) between multiple subnets with uncertain disturbances. Finally, Semiconductor Lasers chaos system is taken as node dynamics to construct small-world networks for inner and outer synchronization simulations. And the simulation results verify the feasibility and effectiveness of the proposed method.