Nonseparation analysis-based finite/fixed-time synchronization of fully complex-valued impulsive dynamical networks

In this article, the impulsive effect is introduced into complex-variable networks (CO-VNs) and the finite/fixed-time synchronization (FI-T/FX-TS) of fully CO-VNs is discussed without using the classical decomposition approach. First of all, by applying the comparison principle, mathematical induction and the optimization method, two theorems are established to realize FI/FX-T stability of impulsive systems, and the estimated convergence time derived is more accurate. Furthermore, under the vector-valued signum function and different forms of norms in the complex field, several complex-valued control protocols are directly designed to realize synchronization. Besides, some effective conditions for FI/FX-TS are derived under the improved FI/FX-T stability results, which are simpler and easier to be verified than the previous decomposition results. To conclude, three numerical examples are provided to verify the obtained theoretical results.