Distributed Synchronization Control on Complex Dynamical Networks with Multiple Delay and Hybrid Impluses

In this study, we investigate the issue of achieving global exponential synchronization for a specific type of complex networks that exhibit time-varying delays. We consider both system delays and discrete delays in our analysis. To address these challenges, we propose an efficient delayed impulsive control strategy. This strategy relies solely on the state information of other nodes that has undergone weighted averaging, making it highly practical for implementation. By employing the Lyapunov stability theory and mathematical induction, we derive sufficient conditions that ensure the global exponential synchronization of the complex networks. Finally, we present a numerical simulation that demonstrates the efficacy of the derived criteria and the practicality of the proposed delayed impulsive control scheme.